diff --git a/NEWS.md b/NEWS.md
index db86c00b8e20b..746ac5ec74944 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -44,6 +44,10 @@ Language changes
   * The syntax for parametric methods, `function f{T}(x::T)`, has been
     changed to `function f(x::T) where {T}` ([#11310]).
 
+  * The fallback constructor that calls `convert` is deprecated. Instead, new types should
+    prefer to define constructors, and add `convert` methods that call those constructors
+    only as necessary ([#15120]).
+
   * The syntax `1.+2` is deprecated, since it is ambiguous: it could mean either
     `1 .+ 2` (the current meaning) or `1. + 2` ([#19089]).
 
diff --git a/base/Enums.jl b/base/Enums.jl
index 83c9afab5bdb3..48c7233178359 100644
--- a/base/Enums.jl
+++ b/base/Enums.jl
@@ -9,8 +9,8 @@ function basetype end
 
 abstract type Enum{T<:Integer} end
 
-Base.convert(::Type{Integer}, x::Enum{T}) where {T<:Integer} = bitcast(T, x)
-Base.convert(::Type{T}, x::Enum{T2}) where {T<:Integer,T2<:Integer} = convert(T, bitcast(T2, x))
+(::Type{T})(x::Enum{T2}) where {T<:Integer,T2<:Integer} = T(bitcast(T2, x))::T
+Base.cconvert(::Type{T}, x::Enum{T2}) where {T<:Integer,T2<:Integer} = T(x)
 Base.write(io::IO, x::Enum{T}) where {T<:Integer} = write(io, T(x))
 Base.read(io::IO, ::Type{T}) where {T<:Enum} = T(read(io, Enums.basetype(T)))
 
@@ -106,7 +106,7 @@ macro enum(T, syms...)
     blk = quote
         # enum definition
         Base.@__doc__(primitive type $(esc(typename)) <: Enum{$(basetype)} $(sizeof(basetype) * 8) end)
-        function Base.convert(::Type{$(esc(typename))}, x::Integer)
+        function $(esc(typename))(x::Integer)
             $(membershiptest(:x, values)) || enum_argument_error($(Expr(:quote, typename)), x)
             return bitcast($(esc(typename)), convert($(basetype), x))
         end
diff --git a/base/abstractarray.jl b/base/abstractarray.jl
index c998dca6cccce..00414ecacf6d7 100644
--- a/base/abstractarray.jl
+++ b/base/abstractarray.jl
@@ -11,6 +11,17 @@ Supertype for `N`-dimensional arrays (or array-like types) with elements of type
 """
 AbstractArray
 
+convert(::Type{T}, a::T) where {T<:AbstractArray} = a
+convert(::Type{T}, a::AbstractArray) where {T<:AbstractArray} = T(a)
+
+if module_name(@__MODULE__) === :Base  # avoid method overwrite
+# catch undefined constructors before the deprecation kicks in
+# TODO: remove when deprecation is removed
+function (::Type{T})(arg) where {T<:AbstractArray}
+    throw(MethodError(T, (arg,)))
+end
+end
+
 """
     size(A::AbstractArray, [dim...])
 
@@ -854,14 +865,6 @@ isempty(a::AbstractArray) = (_length(a) == 0)
 # keys with an IndexStyle
 keys(s::IndexStyle, A::AbstractArray, B::AbstractArray...) = eachindex(s, A, B...)
 
-## Conversions ##
-
-convert(::Type{AbstractArray{T,N}}, A::AbstractArray{T,N}) where {T,N  } = A
-convert(::Type{AbstractArray{T,N}}, A::AbstractArray{S,N}) where {T,S,N} = copyto!(similar(A,T), A)
-convert(::Type{AbstractArray{T}},   A::AbstractArray{S,N}) where {T,S,N} = convert(AbstractArray{T,N}, A)
-
-convert(::Type{Array}, A::AbstractArray{T,N}) where {T,N} = convert(Array{T,N}, A)
-
 """
    of_indices(x, y)
 
diff --git a/base/abstractdict.jl b/base/abstractdict.jl
index bdcd083c2084c..d688a6b9023c4 100644
--- a/base/abstractdict.jl
+++ b/base/abstractdict.jl
@@ -502,6 +502,17 @@ push!(t::AbstractDict, p::Pair) = setindex!(t, p.second, p.first)
 push!(t::AbstractDict, p::Pair, q::Pair) = push!(push!(t, p), q)
 push!(t::AbstractDict, p::Pair, q::Pair, r::Pair...) = push!(push!(push!(t, p), q), r...)
 
+# AbstractDicts are convertible
+convert(::Type{T}, x::T) where {T<:AbstractDict} = x
+
+function convert(::Type{T}, x::AbstractDict) where T<:AbstractDict
+    h = T(x)
+    if length(h) != length(x)
+        error("key collision during dictionary conversion")
+    end
+    return h
+end
+
 # hashing objects by identity
 
 """
diff --git a/base/array.jl b/base/array.jl
index fb7925e37482b..7cef7f61c21ee 100644
--- a/base/array.jl
+++ b/base/array.jl
@@ -381,7 +381,7 @@ function ones end
 
 for (fname, felt) in ((:zeros, :zero), (:ones, :one))
     @eval begin
-        $fname(::Type{T}, dims::NTuple{N, Any}) where {T, N} = fill!(Array{T,N}(uninitialized, Dims(dims)), $felt(T))
+        $fname(::Type{T}, dims::NTuple{N, Any}) where {T, N} = fill!(Array{T,N}(uninitialized, convert(Dims, dims)::Dims), $felt(T))
         $fname(dims::Tuple) = ($fname)(Float64, dims)
         $fname(::Type{T}, dims...) where {T} = $fname(T, dims)
         $fname(dims...) = $fname(dims)
@@ -402,21 +402,14 @@ oneunit(x::AbstractMatrix{T}) where {T} = _one(oneunit(T), x)
 # arises in similar(dest, Pair{Union{},Union{}}) where dest::Dict:
 convert(::Type{Vector{Union{}}}, a::Vector{Union{}}) = a
 
-convert(::Type{Vector}, x::AbstractVector{T}) where {T} = convert(Vector{T}, x)
-convert(::Type{Matrix}, x::AbstractMatrix{T}) where {T} = convert(Matrix{T}, x)
-
-convert(::Type{Array{T}}, x::Array{T,n}) where {T,n} = x
-convert(::Type{Array{T,n}}, x::Array{T,n}) where {T,n} = x
-
-convert(::Type{Array{T}}, x::AbstractArray{S,n}) where {T,n,S} = convert(Array{T,n}, x)
-convert(::Type{Array{T,n}}, x::AbstractArray{S,n}) where {T,n,S} = copyto!(Array{T,n}(uninitialized, size(x)), x)
-
 promote_rule(a::Type{Array{T,n}}, b::Type{Array{S,n}}) where {T,n,S} = el_same(promote_type(T,S), a, b)
 
-# constructors should make copies
+## Constructors ##
 
 if module_name(@__MODULE__) === :Base  # avoid method overwrite
-(::Type{T})(x::T) where {T<:Array} = copy(x)
+# constructors should make copies
+Array{T,N}(x::AbstractArray{S,N})         where {T,N,S} = copyto!(Array{T,N}(uninitialized, size(x)), x)
+AbstractArray{T,N}(A::AbstractArray{S,N}) where {T,N,S} = copyto!(similar(A,T), A)
 end
 
 ## copying iterators to containers
@@ -504,14 +497,26 @@ end
 # gets a chance to see it, so that recursive calls to the caller
 # don't trigger the inference limiter
 if isdefined(Core, :Inference)
-    macro default_eltype(itrt)
+    macro default_eltype(itr)
+        I = esc(itr)
         return quote
-            Core.Inference.return_type(first, Tuple{$(esc(itrt))})
+            if $I isa Generator && ($I).f isa Type
+                ($I).f
+            else
+                Core.Inference.return_type(first, Tuple{typeof($I)})
+            end
         end
     end
 else
-    macro default_eltype(itrt)
-        return :(Any)
+    macro default_eltype(itr)
+        I = esc(itr)
+        return quote
+            if $I isa Generator && ($I).f isa Type
+                ($I).f
+            else
+                Any
+            end
+        end
     end
 end
 
@@ -520,7 +525,7 @@ _array_for(::Type{T}, itr, ::HasShape) where {T} = similar(Array{T}, axes(itr)):
 
 function collect(itr::Generator)
     isz = iteratorsize(itr.iter)
-    et = @default_eltype(typeof(itr))
+    et = @default_eltype(itr)
     if isa(isz, SizeUnknown)
         return grow_to!(Vector{et}(), itr)
     else
@@ -534,12 +539,12 @@ function collect(itr::Generator)
 end
 
 _collect(c, itr, ::EltypeUnknown, isz::SizeUnknown) =
-    grow_to!(_similar_for(c, @default_eltype(typeof(itr)), itr, isz), itr)
+    grow_to!(_similar_for(c, @default_eltype(itr), itr, isz), itr)
 
 function _collect(c, itr, ::EltypeUnknown, isz::Union{HasLength,HasShape})
     st = start(itr)
     if done(itr,st)
-        return _similar_for(c, @default_eltype(typeof(itr)), itr, isz)
+        return _similar_for(c, @default_eltype(itr), itr, isz)
     end
     v1, st = next(itr, st)
     collect_to_with_first!(_similar_for(c, typeof(v1), itr, isz), v1, itr, st)
diff --git a/base/asyncmap.jl b/base/asyncmap.jl
index 83b3c25579271..b92ba3cf3c43b 100644
--- a/base/asyncmap.jl
+++ b/base/asyncmap.jl
@@ -248,7 +248,7 @@ end
 function asyncmap(f, s::AbstractString; kwargs...)
     s2 = Vector{Char}(uninitialized, length(s))
     asyncmap!(f, s2, s; kwargs...)
-    return convert(String, s2)
+    return String(s2)
 end
 
 # map on a single BitArray returns a BitArray if the mapping function is boolean.
diff --git a/base/bitarray.jl b/base/bitarray.jl
index 9da097162ace0..d3f57f063d474 100644
--- a/base/bitarray.jl
+++ b/base/bitarray.jl
@@ -449,12 +449,10 @@ function _bitreshape(B::BitArray, dims::NTuple{N,Int}) where N
     return Br
 end
 
-## Conversions ##
+## Constructors ##
 
-convert(::Type{Array{T}}, B::BitArray{N}) where {T,N} = convert(Array{T,N}, B)
-convert(::Type{Array{T,N}}, B::BitArray{N}) where {T,N} = _convert(Array{T,N}, B) # see #15801
-function _convert(::Type{Array{T,N}}, B::BitArray{N}) where {T,N}
-    A = Array{T}(uninitialized, size(B))
+function Array{T,N}(B::BitArray{N}) where {T,N}
+    A = Array{T,N}(uninitialized, size(B))
     Bc = B.chunks
     @inbounds for i = 1:length(A)
         A[i] = unsafe_bitgetindex(Bc, i)
@@ -462,8 +460,8 @@ function _convert(::Type{Array{T,N}}, B::BitArray{N}) where {T,N}
     return A
 end
 
-convert(::Type{BitArray}, A::AbstractArray{T,N}) where {T,N} = convert(BitArray{N}, A)
-function convert(::Type{BitArray{N}}, A::AbstractArray{T,N}) where N where T
+BitArray(A::AbstractArray{<:Any,N}) where {N} = BitArray{N}(A)
+function BitArray{N}(A::AbstractArray{T,N}) where N where T
     B = BitArray(uninitialized, size(A))
     Bc = B.chunks
     l = length(B)
@@ -488,7 +486,7 @@ function convert(::Type{BitArray{N}}, A::AbstractArray{T,N}) where N where T
     return B
 end
 
-function convert(::Type{BitArray{N}}, A::Array{Bool,N}) where N
+function BitArray{N}(A::Array{Bool,N}) where N
     B = BitArray(uninitialized, size(A))
     Bc = B.chunks
     l = length(B)
@@ -497,16 +495,9 @@ function convert(::Type{BitArray{N}}, A::Array{Bool,N}) where N
     return B
 end
 
-convert(::Type{BitArray{N}}, B::BitArray{N}) where {N} = B
-convert(::Type{AbstractArray{T,N}}, B::BitArray{N}) where {T,N} = convert(Array{T,N}, B)
-
 reinterpret(::Type{Bool}, B::BitArray, dims::NTuple{N,Int}) where {N} = reinterpret(B, dims)
 reinterpret(B::BitArray, dims::NTuple{N,Int}) where {N} = reshape(B, dims)
 
-## Constructors from generic iterables ##
-
-BitArray(A::AbstractArray{<:Any,N}) where {N} = convert(BitArray{N}, A)
-
 if module_name(@__MODULE__) === :Base  # avoid method overwrite
 (::Type{T})(x::T) where {T<:BitArray} = copy(x)
 end
diff --git a/base/bool.jl b/base/bool.jl
index be60d2758337e..135390cdf9859 100644
--- a/base/bool.jl
+++ b/base/bool.jl
@@ -1,11 +1,5 @@
 # This file is a part of Julia. License is MIT: https://julialang.org/license
 
-## boolean conversions ##
-
-convert(::Type{Bool}, x::Bool) = x
-convert(::Type{Bool}, x::Float16) = x==0 ? false : x==1 ? true : throw(InexactError(:convert, Bool, x))
-convert(::Type{Bool}, x::Real) = x==0 ? false : x==1 ? true : throw(InexactError(:convert, Bool, x))
-
 # promote Bool to any other numeric type
 promote_rule(::Type{Bool}, ::Type{T}) where {T<:Number} = T
 
diff --git a/base/boot.jl b/base/boot.jl
index d9194a79f1b87..900a82c588229 100644
--- a/base/boot.jl
+++ b/base/boot.jl
@@ -204,6 +204,10 @@ struct ErrorException <: Exception
     msg::AbstractString
 end
 
+macro _inline_meta()
+    Expr(:meta, :inline)
+end
+
 macro _noinline_meta()
     Expr(:meta, :noinline)
 end
@@ -382,6 +386,13 @@ Array{T}(::Uninitialized, d::NTuple{N,Int}) where {T,N} = Array{T,N}(uninitializ
 Array{T,1}() where {T} = Array{T,1}(uninitialized, 0)
 
 
+(::Type{Array{T,N} where T})(x::AbstractArray{S,N}) where {S,N} = Array{S,N}(x)
+
+Array(A::AbstractArray{T,N})    where {T,N}   = Array{T,N}(A)
+Array{T}(A::AbstractArray{S,N}) where {T,N,S} = Array{T,N}(A)
+
+AbstractArray{T}(A::AbstractArray{S,N}) where {T,S,N} = AbstractArray{T,N}(A)
+
 # primitive Symbol constructors
 function Symbol(s::String)
     return ccall(:jl_symbol_n, Ref{Symbol}, (Ptr{UInt8}, Int),
@@ -508,4 +519,197 @@ function NamedTuple{names,T}(args::T) where {names, T <: Tuple}
     end
 end
 
+# constructors for built-in types
+
+import .Intrinsics: eq_int, trunc_int, lshr_int, sub_int, shl_int, bitcast, sext_int, zext_int, and_int
+
+throw_inexacterror(f::Symbol, T::Type, val) = (@_noinline_meta; throw(InexactError(f, T, val)))
+
+function is_top_bit_set(x)
+    @_inline_meta
+    eq_int(trunc_int(Int8, lshr_int(x, sub_int(shl_int(sizeof(x), 3), 1))), trunc_int(Int8, 1))
+end
+
+function is_top_bit_set(x::Union{Int8,UInt8})
+    @_inline_meta
+    eq_int(lshr_int(x, 7), trunc_int(typeof(x), 1))
+end
+
+function check_top_bit(x)
+    @_inline_meta
+    is_top_bit_set(x) && throw_inexacterror(:check_top_bit, typeof(x), x)
+    x
+end
+
+function checked_trunc_sint(::Type{To}, x::From) where {To,From}
+    @_inline_meta
+    y = trunc_int(To, x)
+    back = sext_int(From, y)
+    eq_int(x, back) || throw_inexacterror(:trunc, To, x)
+    y
+end
+
+function checked_trunc_uint(::Type{To}, x::From) where {To,From}
+    @_inline_meta
+    y = trunc_int(To, x)
+    back = zext_int(From, y)
+    eq_int(x, back) || throw_inexacterror(:trunc, To, x)
+    y
+end
+
+toInt8(x::Int8)       = x
+toInt8(x::Int16)      = checked_trunc_sint(Int8, x)
+toInt8(x::Int32)      = checked_trunc_sint(Int8, x)
+toInt8(x::Int64)      = checked_trunc_sint(Int8, x)
+toInt8(x::Int128)     = checked_trunc_sint(Int8, x)
+toInt8(x::UInt8)      = bitcast(Int8, check_top_bit(x))
+toInt8(x::UInt16)     = checked_trunc_sint(Int8, check_top_bit(x))
+toInt8(x::UInt32)     = checked_trunc_sint(Int8, check_top_bit(x))
+toInt8(x::UInt64)     = checked_trunc_sint(Int8, check_top_bit(x))
+toInt8(x::UInt128)    = checked_trunc_sint(Int8, check_top_bit(x))
+toInt8(x::Bool)       = and_int(zext_int(Int8, x), Int8(1))
+toInt16(x::Int8)      = sext_int(Int16, x)
+toInt16(x::Int16)     = x
+toInt16(x::Int32)     = checked_trunc_sint(Int16, x)
+toInt16(x::Int64)     = checked_trunc_sint(Int16, x)
+toInt16(x::Int128)    = checked_trunc_sint(Int16, x)
+toInt16(x::UInt8)     = zext_int(Int16, x)
+toInt16(x::UInt16)    = bitcast(Int16, check_top_bit(x))
+toInt16(x::UInt32)    = checked_trunc_sint(Int16, check_top_bit(x))
+toInt16(x::UInt64)    = checked_trunc_sint(Int16, check_top_bit(x))
+toInt16(x::UInt128)   = checked_trunc_sint(Int16, check_top_bit(x))
+toInt16(x::Bool)      = and_int(zext_int(Int16, x), Int16(1))
+toInt32(x::Int8)      = sext_int(Int32, x)
+toInt32(x::Int16)     = sext_int(Int32, x)
+toInt32(x::Int32)     = x
+toInt32(x::Int64)     = checked_trunc_sint(Int32, x)
+toInt32(x::Int128)    = checked_trunc_sint(Int32, x)
+toInt32(x::UInt8)     = zext_int(Int32, x)
+toInt32(x::UInt16)    = zext_int(Int32, x)
+toInt32(x::UInt32)    = bitcast(Int32, check_top_bit(x))
+toInt32(x::UInt64)    = checked_trunc_sint(Int32, check_top_bit(x))
+toInt32(x::UInt128)   = checked_trunc_sint(Int32, check_top_bit(x))
+toInt32(x::Bool)      = and_int(zext_int(Int32, x), Int32(1))
+toInt64(x::Int8)      = sext_int(Int64, x)
+toInt64(x::Int16)     = sext_int(Int64, x)
+toInt64(x::Int32)     = sext_int(Int64, x)
+toInt64(x::Int64)     = x
+toInt64(x::Int128)    = checked_trunc_sint(Int64, x)
+toInt64(x::UInt8)     = zext_int(Int64, x)
+toInt64(x::UInt16)    = zext_int(Int64, x)
+toInt64(x::UInt32)    = zext_int(Int64, x)
+toInt64(x::UInt64)    = bitcast(Int64, check_top_bit(x))
+toInt64(x::UInt128)   = checked_trunc_sint(Int64, check_top_bit(x))
+toInt64(x::Bool)      = and_int(zext_int(Int64, x), Int64(1))
+toInt128(x::Int8)     = sext_int(Int128, x)
+toInt128(x::Int16)    = sext_int(Int128, x)
+toInt128(x::Int32)    = sext_int(Int128, x)
+toInt128(x::Int64)    = sext_int(Int128, x)
+toInt128(x::Int128)   = x
+toInt128(x::UInt8)    = zext_int(Int128, x)
+toInt128(x::UInt16)   = zext_int(Int128, x)
+toInt128(x::UInt32)   = zext_int(Int128, x)
+toInt128(x::UInt64)   = zext_int(Int128, x)
+toInt128(x::UInt128)  = bitcast(Int128, check_top_bit(x))
+toInt128(x::Bool)     = and_int(zext_int(Int128, x), Int128(1))
+toUInt8(x::Int8)      = bitcast(UInt8, check_top_bit(x))
+toUInt8(x::Int16)     = checked_trunc_uint(UInt8, x)
+toUInt8(x::Int32)     = checked_trunc_uint(UInt8, x)
+toUInt8(x::Int64)     = checked_trunc_uint(UInt8, x)
+toUInt8(x::Int128)    = checked_trunc_uint(UInt8, x)
+toUInt8(x::UInt8)     = x
+toUInt8(x::UInt16)    = checked_trunc_uint(UInt8, x)
+toUInt8(x::UInt32)    = checked_trunc_uint(UInt8, x)
+toUInt8(x::UInt64)    = checked_trunc_uint(UInt8, x)
+toUInt8(x::UInt128)   = checked_trunc_uint(UInt8, x)
+toUInt8(x::Bool)      = and_int(zext_int(UInt8, x), UInt8(1))
+toUInt16(x::Int8)     = sext_int(UInt16, check_top_bit(x))
+toUInt16(x::Int16)    = bitcast(UInt16, check_top_bit(x))
+toUInt16(x::Int32)    = checked_trunc_uint(UInt16, x)
+toUInt16(x::Int64)    = checked_trunc_uint(UInt16, x)
+toUInt16(x::Int128)   = checked_trunc_uint(UInt16, x)
+toUInt16(x::UInt8)    = zext_int(UInt16, x)
+toUInt16(x::UInt16)   = x
+toUInt16(x::UInt32)   = checked_trunc_uint(UInt16, x)
+toUInt16(x::UInt64)   = checked_trunc_uint(UInt16, x)
+toUInt16(x::UInt128)  = checked_trunc_uint(UInt16, x)
+toUInt16(x::Bool)     = and_int(zext_int(UInt16, x), UInt16(1))
+toUInt32(x::Int8)     = sext_int(UInt32, check_top_bit(x))
+toUInt32(x::Int16)    = sext_int(UInt32, check_top_bit(x))
+toUInt32(x::Int32)    = bitcast(UInt32, check_top_bit(x))
+toUInt32(x::Int64)    = checked_trunc_uint(UInt32, x)
+toUInt32(x::Int128)   = checked_trunc_uint(UInt32, x)
+toUInt32(x::UInt8)    = zext_int(UInt32, x)
+toUInt32(x::UInt16)   = zext_int(UInt32, x)
+toUInt32(x::UInt32)   = x
+toUInt32(x::UInt64)   = checked_trunc_uint(UInt32, x)
+toUInt32(x::UInt128)  = checked_trunc_uint(UInt32, x)
+toUInt32(x::Bool)     = and_int(zext_int(UInt32, x), UInt32(1))
+toUInt64(x::Int8)     = sext_int(UInt64, check_top_bit(x))
+toUInt64(x::Int16)    = sext_int(UInt64, check_top_bit(x))
+toUInt64(x::Int32)    = sext_int(UInt64, check_top_bit(x))
+toUInt64(x::Int64)    = bitcast(UInt64, check_top_bit(x))
+toUInt64(x::Int128)   = checked_trunc_uint(UInt64, x)
+toUInt64(x::UInt8)    = zext_int(UInt64, x)
+toUInt64(x::UInt16)   = zext_int(UInt64, x)
+toUInt64(x::UInt32)   = zext_int(UInt64, x)
+toUInt64(x::UInt64)   = x
+toUInt64(x::UInt128)  = checked_trunc_uint(UInt64, x)
+toUInt64(x::Bool)     = and_int(zext_int(UInt64, x), UInt64(1))
+toUInt128(x::Int8)    = sext_int(UInt128, check_top_bit(x))
+toUInt128(x::Int16)   = sext_int(UInt128, check_top_bit(x))
+toUInt128(x::Int32)   = sext_int(UInt128, check_top_bit(x))
+toUInt128(x::Int64)   = sext_int(UInt128, check_top_bit(x))
+toUInt128(x::Int128)  = bitcast(UInt128, check_top_bit(x))
+toUInt128(x::UInt8)   = zext_int(UInt128, x)
+toUInt128(x::UInt16)  = zext_int(UInt128, x)
+toUInt128(x::UInt32)  = zext_int(UInt128, x)
+toUInt128(x::UInt64)  = zext_int(UInt128, x)
+toUInt128(x::UInt128) = x
+toUInt128(x::Bool)    = and_int(zext_int(UInt128, x), UInt128(1))
+
+# TODO: this is here to work around the 4 method limit in inference (#23210).
+const BuiltinInts = Union{Int128, Int16, Int32, Int64, Int8, UInt128, UInt16, UInt32, UInt64, UInt8, Bool}
+Int8(x::BuiltinInts)    = toInt8(x)::Int8
+Int16(x::BuiltinInts)   = toInt16(x)::Int16
+Int32(x::BuiltinInts)   = toInt32(x)::Int32
+Int64(x::BuiltinInts)   = toInt64(x)::Int64
+Int128(x::BuiltinInts)  = toInt128(x)::Int128
+UInt8(x::BuiltinInts)   = toUInt8(x)::UInt8
+UInt16(x::BuiltinInts)  = toUInt16(x)::UInt16
+UInt32(x::BuiltinInts)  = toUInt32(x)::UInt32
+UInt64(x::BuiltinInts)  = toUInt64(x)::UInt64
+UInt128(x::BuiltinInts) = toUInt128(x)::UInt128
+
+Char(x::Number) = Char(UInt32(x))
+Char(x::Char) = x
+(::Type{T})(x::Char) where {T<:Number} = T(UInt32(x))
+
+(::Type{T})(x::T) where {T<:Number} = x
+
+Int(x::Ptr)  = bitcast(Int, x)
+UInt(x::Ptr) = bitcast(UInt, x)
+if Int === Int32
+Int64(x::Ptr) = Int64(UInt32(x))
+UInt64(x::Ptr) = UInt64(UInt32(x))
+end
+Ptr{T}(x::Union{Int,UInt,Ptr}) where {T} = bitcast(Ptr{T}, x)
+
+Signed(x::UInt8)    = Int8(x)
+Unsigned(x::Int8)   = UInt8(x)
+Signed(x::UInt16)   = Int16(x)
+Unsigned(x::Int16)  = UInt16(x)
+Signed(x::UInt32)   = Int32(x)
+Unsigned(x::Int32)  = UInt32(x)
+Signed(x::UInt64)   = Int64(x)
+Unsigned(x::Int64)  = UInt64(x)
+Signed(x::UInt128)  = Int128(x)
+Unsigned(x::Int128) = UInt128(x)
+
+Signed(x::Union{Float32, Float64, Bool})   = Int(x)
+Unsigned(x::Union{Float32, Float64, Bool}) = UInt(x)
+
+Integer(x::Integer) = x
+Integer(x::Union{Float32, Float64}) = Int(x)
+
 ccall(:jl_set_istopmod, Cvoid, (Any, Bool), Core, true)
diff --git a/base/c.jl b/base/c.jl
index 8972a809d1e11..61163a93fcbc4 100644
--- a/base/c.jl
+++ b/base/c.jl
@@ -90,14 +90,16 @@ Cwchar_t
     end
 end
 
-# construction from typed pointers
-convert(::Type{Cstring}, p::Ptr{<:Union{Int8,UInt8}}) = bitcast(Cstring, p)
-convert(::Type{Cwstring}, p::Ptr{Cwchar_t}) = bitcast(Cwstring, p)
-convert(::Type{Ptr{T}}, p::Cstring) where {T<:Union{Int8,UInt8}} = bitcast(Ptr{T}, p)
-convert(::Type{Ptr{Cwchar_t}}, p::Cwstring) = bitcast(Ptr{Cwchar_t}, p)
+# construction from pointers
+Cstring(p::Union{Ptr{Int8},Ptr{UInt8},Ptr{Cvoid}}) = bitcast(Cstring, p)
+Cwstring(p::Union{Ptr{Cwchar_t},Ptr{Cvoid}})       = bitcast(Cwstring, p)
+(::Type{Ptr{T}})(p::Cstring) where {T<:Union{Int8,UInt8,Cvoid}} = bitcast(Ptr{T}, p)
+(::Type{Ptr{T}})(p::Cwstring) where {T<:Union{Cwchar_t,Cvoid}}  = bitcast(Ptr{Cwchar_t}, p)
 
-# construction from untyped pointers
-convert(::Type{T}, p::Ptr{Cvoid}) where {T<:Union{Cstring,Cwstring}} = bitcast(T, p)
+convert(::Type{Cstring}, p::Union{Ptr{Int8},Ptr{UInt8},Ptr{Cvoid}}) = Cstring(p)
+convert(::Type{Cwstring}, p::Union{Ptr{Cwchar_t},Ptr{Cvoid}}) = Cwstring(p)
+convert(::Type{Ptr{T}}, p::Cstring) where {T<:Union{Int8,UInt8,Cvoid}} = Ptr{T}(p)
+convert(::Type{Ptr{T}}, p::Cwstring) where {T<:Union{Cwchar_t,Cvoid}} = Ptr{T}(p)
 
 """
     pointer(array [, index])
@@ -157,7 +159,8 @@ function unsafe_convert(::Type{Cwstring}, v::Vector{Cwchar_t})
 end
 
 # symbols are guaranteed not to contain embedded NUL
-convert(::Type{Cstring}, s::Symbol) = Cstring(unsafe_convert(Ptr{Cchar}, s))
+cconvert(::Type{Cstring}, s::Symbol) = s
+unsafe_convert(::Type{Cstring}, s::Symbol) = Cstring(unsafe_convert(Ptr{Cchar}, s))
 
 @static if ccall(:jl_get_UNAME, Any, ()) === :NT
 """
diff --git a/base/char.jl b/base/char.jl
index 0a6cab5b4b8ac..7c7595309aa7a 100644
--- a/base/char.jl
+++ b/base/char.jl
@@ -22,7 +22,7 @@ function isoverlong(c::Char)
     (u >> 24 == 0xc0) | (u >> 21 == 0x0704) | (u >> 20 == 0x0f08)
 end
 
-function convert(::Type{UInt32}, c::Char)
+function UInt32(c::Char)
     # TODO: use optimized inline LLVM
     u = reinterpret(UInt32, c)
     u < 0x80000000 && return reinterpret(UInt32, u >> 24)
@@ -37,7 +37,7 @@ function convert(::Type{UInt32}, c::Char)
     (u & 0x007f0000 >> 4) | (u & 0x7f000000 >> 6)
 end
 
-function convert(::Type{Char}, u::UInt32)
+function Char(u::UInt32)
     u < 0x80 && return reinterpret(Char, u << 24)
     u < 0x00200000 || code_point_err(u)::Union{}
     c = ((u << 0) & 0x0000003f) | ((u << 2) & 0x00003f00) |
@@ -48,17 +48,17 @@ function convert(::Type{Char}, u::UInt32)
     reinterpret(Char, c)
 end
 
-function convert(::Type{T}, c::Char) where T <: Union{Int8,UInt8}
+function (T::Union{Type{Int8},Type{UInt8}})(c::Char)
     i = reinterpret(Int32, c)
     i ≥ 0 ? ((i >>> 24) % T) : T(UInt32(c))
 end
 
-function convert(::Type{Char}, b::Union{Int8,UInt8})
+function Char(b::Union{Int8,UInt8})
     0 ≤ b ≤ 0x7f ? reinterpret(Char, (b % UInt32) << 24) : Char(UInt32(b))
 end
 
-convert(::Type{Char}, x::Number) = Char(UInt32(x))
-convert(::Type{T}, x::Char) where {T<:Number} = convert(T, UInt32(x))
+convert(::Type{Char}, x::Number) = Char(x)
+convert(::Type{T}, x::Char) where {T<:Number} = T(x)
 
 rem(x::Char, ::Type{T}) where {T<:Number} = rem(UInt32(x), T)
 
diff --git a/base/complex.jl b/base/complex.jl
index 1ea172e6f8a7a..0ef1255ebeff3 100644
--- a/base/complex.jl
+++ b/base/complex.jl
@@ -32,13 +32,12 @@ const ComplexF64  = Complex{Float64}
 const ComplexF32  = Complex{Float32}
 const ComplexF16  = Complex{Float16}
 
-convert(::Type{Complex{T}}, x::Real) where {T<:Real} = Complex{T}(x,0)
-convert(::Type{Complex{T}}, z::Complex) where {T<:Real} = Complex{T}(real(z),imag(z))
-convert(::Type{T}, z::Complex) where {T<:Real} =
-    isreal(z) ? convert(T,real(z)) : throw(InexactError(:convert, T, z))
+Complex{T}(x::Real) where {T<:Real} = Complex{T}(x,0)
+Complex{T}(z::Complex) where {T<:Real} = Complex{T}(real(z),imag(z))
+(::Type{T})(z::Complex) where {T<:Real} =
+    isreal(z) ? T(real(z))::T : throw(InexactError(Symbol(string(T)), T, z))
 
-convert(::Type{Complex}, z::Complex) = z
-convert(::Type{Complex}, x::Real) = Complex(x)
+Complex(z::Complex) = z
 
 promote_rule(::Type{Complex{T}}, ::Type{S}) where {T<:Real,S<:Real} =
     Complex{promote_type(T,S)}
diff --git a/base/coreimg.jl b/base/coreimg.jl
index de91ed1536975..685e73a936d45 100644
--- a/base/coreimg.jl
+++ b/base/coreimg.jl
@@ -15,9 +15,6 @@ eval(m, x) = Core.eval(m, x)
 include(x) = Core.include(Inference, x)
 include(mod, x) = Core.include(mod, x)
 
-# conditional to allow redefining Core.Inference after base exists
-isdefined(Main, :Base) || ((::Type{T})(arg) where {T} = convert(T, arg)::T)
-
 function return_type end
 
 ## Load essential files and libraries
diff --git a/base/deprecated.jl b/base/deprecated.jl
index a392412da5863..811a091966221 100644
--- a/base/deprecated.jl
+++ b/base/deprecated.jl
@@ -1552,6 +1552,35 @@ export hex2num
 @deprecate convert(::Type{String}, s::Symbol)                 String(s)
 @deprecate convert(::Type{String}, v::Vector{UInt8})          String(v)
 @deprecate convert(::Type{S}, g::Unicode.GraphemeIterator) where {S<:AbstractString}  convert(S, g.s)
+@deprecate convert(::Type{String}, v::AbstractVector{Char})   String(v)
+
+@deprecate convert(::Type{UInt128},     u::Random.UUID)     UInt128(u)
+@deprecate convert(::Type{Random.UUID}, s::AbstractString)  Random.UUID(s)
+@deprecate convert(::Type{Libc.FILE}, s::IO)  Libc.FILE(s)
+@deprecate convert(::Type{VersionNumber}, v::Integer)         VersionNumber(v)
+@deprecate convert(::Type{VersionNumber}, v::Tuple)           VersionNumber(v)
+@deprecate convert(::Type{VersionNumber}, v::AbstractString)  VersionNumber(v)
+
+@deprecate (convert(::Type{Integer}, x::Enum{T}) where {T<:Integer})         Integer(x)
+@deprecate (convert(::Type{T}, x::Enum{T2}) where {T<:Integer,T2<:Integer})  T(x)
+
+@deprecate convert(dt::Type{<:Integer}, ip::IPAddr)  dt(ip)
+
+function (::Type{T})(arg) where {T}
+    if applicable(convert, T, arg)
+        sig = which(convert, (Type{T}, typeof(arg))).sig
+        if sig == (Tuple{typeof(convert),Type{S},Number} where S<:Number) ||
+           sig == (Tuple{typeof(convert),Type{S},AbstractArray} where S<:AbstractArray)
+            # matches a catch-all converter; will stack overflow
+            throw(MethodError(T, (arg,)))
+        end
+        # if `convert` call would not work, just let the method error happen
+        depwarn("Constructors no longer fall back to `convert`. A constructor `$T(::$(typeof(arg)))` should be defined instead.", :Type)
+    end
+    convert(T, arg)::T
+end
+# related items to remove in: abstractarray.jl, dates/periods.jl, inference.jl
+# also remove all uses of is_default_method
 
 # Issue #19923
 @deprecate ror                  circshift
diff --git a/base/dict.jl b/base/dict.jl
index 8815e926b4dea..3e5534885318a 100644
--- a/base/dict.jl
+++ b/base/dict.jl
@@ -159,7 +159,7 @@ dict_with_eltype(DT_apply, ::Type{Pair{K,V}}) where {K,V} = DT_apply(K, V)()
 dict_with_eltype(DT_apply, ::Type) = DT_apply(Any, Any)()
 dict_with_eltype(DT_apply::F, kv, t) where {F} = grow_to!(dict_with_eltype(DT_apply, @default_eltype(typeof(kv))), kv)
 function dict_with_eltype(DT_apply::F, kv::Generator, t) where F
-    T = @default_eltype(typeof(kv))
+    T = @default_eltype(kv)
     if T <: Union{Pair, Tuple{Any, Any}} && _isleaftype(T)
         return dict_with_eltype(DT_apply, kv, T)
     end
@@ -190,21 +190,6 @@ end
 
 empty(a::AbstractDict, ::Type{K}, ::Type{V}) where {K, V} = Dict{K, V}()
 
-# conversion between Dict types
-function convert(::Type{Dict{K,V}},d::AbstractDict) where V where K
-    h = Dict{K,V}()
-    for (k,v) in d
-        ck = convert(K,k)
-        if !haskey(h,ck)
-            h[ck] = convert(V,v)
-        else
-            error("key collision during dictionary conversion")
-        end
-    end
-    return h
-end
-convert(::Type{Dict{K,V}},d::Dict{K,V}) where {K,V} = d
-
 hashindex(key, sz) = (((hash(key)%Int) & (sz-1)) + 1)::Int
 
 @propagate_inbounds isslotempty(h::Dict, i::Int) = h.slots[i] == 0x0
diff --git a/base/float.jl b/base/float.jl
index 9ecd70eb5a976..a441be412b26a 100644
--- a/base/float.jl
+++ b/base/float.jl
@@ -45,7 +45,7 @@ A not-a-number value of type [`Float64`](@ref).
 const NaN = NaN64
 
 ## conversions to floating-point ##
-convert(::Type{Float16}, x::Integer) = convert(Float16, convert(Float32, x))
+Float16(x::Integer) = convert(Float16, convert(Float32, x))
 for t in (Int8, Int16, Int32, Int64, Int128, UInt8, UInt16, UInt32, UInt64, UInt128)
     @eval promote_rule(::Type{Float16}, ::Type{$t}) = Float16
 end
@@ -54,27 +54,27 @@ promote_rule(::Type{Float16}, ::Type{Bool}) = Float16
 for t1 in (Float32, Float64)
     for st in (Int8, Int16, Int32, Int64)
         @eval begin
-            convert(::Type{$t1}, x::($st)) = sitofp($t1, x)
+            (::Type{$t1})(x::($st)) = sitofp($t1, x)
             promote_rule(::Type{$t1}, ::Type{$st}) = $t1
         end
     end
     for ut in (Bool, UInt8, UInt16, UInt32, UInt64)
         @eval begin
-            convert(::Type{$t1}, x::($ut)) = uitofp($t1, x)
+            (::Type{$t1})(x::($ut)) = uitofp($t1, x)
             promote_rule(::Type{$t1}, ::Type{$ut}) = $t1
         end
     end
 end
-convert(::Type{Integer}, x::Float16) = convert(Integer, Float32(x))
-convert(::Type{T}, x::Float16) where {T<:Integer} = convert(T, Float32(x))
+(::Type{T})(x::Float16) where {T<:Integer} = T(Float32(x))
 
+Bool(x::Real) = x==0 ? false : x==1 ? true : throw(InexactError(:Bool, Bool, x))
 
 promote_rule(::Type{Float64}, ::Type{UInt128}) = Float64
 promote_rule(::Type{Float64}, ::Type{Int128}) = Float64
 promote_rule(::Type{Float32}, ::Type{UInt128}) = Float32
 promote_rule(::Type{Float32}, ::Type{Int128}) = Float32
 
-function convert(::Type{Float64}, x::UInt128)
+function Float64(x::UInt128)
     x == 0 && return 0.0
     n = 128-leading_zeros(x) # ndigits0z(x,2)
     if n <= 53
@@ -88,7 +88,7 @@ function convert(::Type{Float64}, x::UInt128)
     reinterpret(Float64, d + y)
 end
 
-function convert(::Type{Float64}, x::Int128)
+function Float64(x::Int128)
     x == 0 && return 0.0
     s = ((x >>> 64) % UInt64) & 0x8000_0000_0000_0000 # sign bit
     x = abs(x) % UInt128
@@ -104,7 +104,7 @@ function convert(::Type{Float64}, x::Int128)
     reinterpret(Float64, s | d + y)
 end
 
-function convert(::Type{Float32}, x::UInt128)
+function Float32(x::UInt128)
     x == 0 && return 0f0
     n = 128-leading_zeros(x) # ndigits0z(x,2)
     if n <= 24
@@ -118,7 +118,7 @@ function convert(::Type{Float32}, x::UInt128)
     reinterpret(Float32, d + y)
 end
 
-function convert(::Type{Float32}, x::Int128)
+function Float32(x::Int128)
     x == 0 && return 0f0
     s = ((x >>> 96) % UInt32) & 0x8000_0000 # sign bit
     x = abs(x) % UInt128
@@ -134,7 +134,7 @@ function convert(::Type{Float32}, x::Int128)
     reinterpret(Float32, s | d + y)
 end
 
-function convert(::Type{Float16}, val::Float32)
+function Float16(val::Float32)
     f = reinterpret(UInt32, val)
     if isnan(val)
         t = 0x8000 ⊻ (0x8000 & ((f >> 0x10) % UInt16))
@@ -157,7 +157,7 @@ function convert(::Type{Float16}, val::Float32)
     reinterpret(Float16, h)
 end
 
-function convert(::Type{Float32}, val::Float16)
+function Float32(val::Float16)
     local ival::UInt32 = reinterpret(UInt16, val)
     local sign::UInt32 = (ival & 0x8000) >> 15
     local exp::UInt32  = (ival & 0x7c00) >> 10
@@ -235,25 +235,28 @@ for i = 0:255
         shifttable[i|0x100+1] = 13
     end
 end
+
 #convert(::Type{Float16}, x::Float32) = fptrunc(Float16, x)
-convert(::Type{Float32}, x::Float64) = fptrunc(Float32, x)
-convert(::Type{Float16}, x::Float64) = convert(Float16, convert(Float32, x))
+Float32(x::Float64) = fptrunc(Float32, x)
+Float16(x::Float64) = Float16(Float32(x))
 
 #convert(::Type{Float32}, x::Float16) = fpext(Float32, x)
-convert(::Type{Float64}, x::Float32) = fpext(Float64, x)
-convert(::Type{Float64}, x::Float16) = convert(Float64, convert(Float32, x))
-
-convert(::Type{AbstractFloat}, x::Bool)    = convert(Float64, x)
-convert(::Type{AbstractFloat}, x::Int8)    = convert(Float64, x)
-convert(::Type{AbstractFloat}, x::Int16)   = convert(Float64, x)
-convert(::Type{AbstractFloat}, x::Int32)   = convert(Float64, x)
-convert(::Type{AbstractFloat}, x::Int64)   = convert(Float64, x) # LOSSY
-convert(::Type{AbstractFloat}, x::Int128)  = convert(Float64, x) # LOSSY
-convert(::Type{AbstractFloat}, x::UInt8)   = convert(Float64, x)
-convert(::Type{AbstractFloat}, x::UInt16)  = convert(Float64, x)
-convert(::Type{AbstractFloat}, x::UInt32)  = convert(Float64, x)
-convert(::Type{AbstractFloat}, x::UInt64)  = convert(Float64, x) # LOSSY
-convert(::Type{AbstractFloat}, x::UInt128) = convert(Float64, x) # LOSSY
+Float64(x::Float32) = fpext(Float64, x)
+Float64(x::Float16) = Float64(Float32(x))
+
+AbstractFloat(x::Bool)    = Float64(x)
+AbstractFloat(x::Int8)    = Float64(x)
+AbstractFloat(x::Int16)   = Float64(x)
+AbstractFloat(x::Int32)   = Float64(x)
+AbstractFloat(x::Int64)   = Float64(x) # LOSSY
+AbstractFloat(x::Int128)  = Float64(x) # LOSSY
+AbstractFloat(x::UInt8)   = Float64(x)
+AbstractFloat(x::UInt16)  = Float64(x)
+AbstractFloat(x::UInt32)  = Float64(x)
+AbstractFloat(x::UInt64)  = Float64(x) # LOSSY
+AbstractFloat(x::UInt128) = Float64(x) # LOSSY
+
+Bool(x::Float16) = x==0 ? false : x==1 ? true : throw(InexactError(:Bool, Bool, x))
 
 """
     float(x)
@@ -261,7 +264,7 @@ convert(::Type{AbstractFloat}, x::UInt128) = convert(Float64, x) # LOSSY
 Convert a number or array to a floating point data type.
 When passed a string, this function is equivalent to `parse(Float64, x)`.
 """
-float(x) = convert(AbstractFloat, x)
+float(x) = AbstractFloat(x)
 
 """
     float(T::Type)
@@ -675,11 +678,11 @@ for Ti in (Int8, Int16, Int32, Int64, Int128, UInt8, UInt16, UInt32, UInt64, UIn
                         throw(InexactError(:trunc, $Ti, x))
                     end
                 end
-                function convert(::Type{$Ti}, x::$Tf)
+                function (::Type{$Ti})(x::$Tf)
                     if ($(Tf(typemin(Ti))) <= x <= $(Tf(typemax(Ti)))) && (trunc(x) == x)
                         return unsafe_trunc($Ti,x)
                     else
-                        throw(InexactError(:convert, $Ti, x))
+                        throw(InexactError($(Expr(:quote,Ti.name.name)), $Ti, x))
                     end
                 end
             end
@@ -696,11 +699,11 @@ for Ti in (Int8, Int16, Int32, Int64, Int128, UInt8, UInt16, UInt32, UInt64, UIn
                         throw(InexactError(:trunc, $Ti, x))
                     end
                 end
-                function convert(::Type{$Ti}, x::$Tf)
+                function (::Type{$Ti})(x::$Tf)
                     if ($(Tf(typemin(Ti))) <= x < $(Tf(typemax(Ti)))) && (trunc(x) == x)
                         return unsafe_trunc($Ti,x)
                     else
-                        throw(InexactError(:convert, $Ti, x))
+                        throw(InexactError($(Expr(:quote,Ti.name.name)), $Ti, x))
                     end
                 end
             end
diff --git a/base/gmp.jl b/base/gmp.jl
index 34895f01d6b2d..1acaa6a10e1f6 100644
--- a/base/gmp.jl
+++ b/base/gmp.jl
@@ -231,8 +231,8 @@ widen(::Type{BigInt})  = BigInt
 
 signed(x::BigInt) = x
 
-convert(::Type{BigInt}, x::BigInt) = x
-convert(::Type{Signed}, x::BigInt) = x
+BigInt(x::BigInt) = x
+Signed(x::BigInt) = x
 
 hastypemax(::Type{BigInt}) = false
 
@@ -262,14 +262,14 @@ function tryparse_internal(::Type{BigInt}, s::AbstractString, startpos::Int, end
     flipsign!(z, sgn)
 end
 
-convert(::Type{BigInt}, x::Union{Clong,Int32}) = MPZ.set_si(x)
-convert(::Type{BigInt}, x::Union{Culong,UInt32}) = MPZ.set_ui(x)
-convert(::Type{BigInt}, x::Bool) = BigInt(UInt(x))
+BigInt(x::Union{Clong,Int32}) = MPZ.set_si(x)
+BigInt(x::Union{Culong,UInt32}) = MPZ.set_ui(x)
+BigInt(x::Bool) = BigInt(UInt(x))
 
 unsafe_trunc(::Type{BigInt}, x::Union{Float32,Float64}) = MPZ.set_d(x)
 
-function convert(::Type{BigInt}, x::Union{Float32,Float64})
-    isinteger(x) || throw(InexactError(:convert, BigInt, x))
+function BigInt(x::Union{Float32,Float64})
+    isinteger(x) || throw(InexactError(:BigInt, BigInt, x))
     unsafe_trunc(BigInt,x)
 end
 
@@ -278,10 +278,10 @@ function trunc(::Type{BigInt}, x::Union{Float32,Float64})
     unsafe_trunc(BigInt,x)
 end
 
-convert(::Type{BigInt}, x::Float16) = BigInt(Float64(x))
-convert(::Type{BigInt}, x::Float32) = BigInt(Float64(x))
+BigInt(x::Float16) = BigInt(Float64(x))
+BigInt(x::Float32) = BigInt(Float64(x))
 
-function convert(::Type{BigInt}, x::Integer)
+function BigInt(x::Integer)
     if x < 0
         if typemin(Clong) <= x
             return BigInt(convert(Clong,x))
@@ -323,26 +323,26 @@ function rem(x::BigInt, ::Type{T}) where T<:Union{Base.BitUnsigned,Base.BitSigne
     flipsign(u, x.size)
 end
 
-rem(x::Integer, ::Type{BigInt}) = convert(BigInt, x)
+rem(x::Integer, ::Type{BigInt}) = BigInt(x)
 
-function convert(::Type{T}, x::BigInt) where T<:Base.BitUnsigned
+function (::Type{T})(x::BigInt) where T<:Base.BitUnsigned
     if sizeof(T) < sizeof(Limb)
         convert(T, convert(Limb,x))
     else
-        0 <= x.size <= cld(sizeof(T),sizeof(Limb)) || throw(InexactError(:convert, T, x))
+        0 <= x.size <= cld(sizeof(T),sizeof(Limb)) || throw(InexactError(Symbol(string(T)), T, x))
         x % T
     end
 end
 
-function convert(::Type{T}, x::BigInt) where T<:Base.BitSigned
+function (::Type{T})(x::BigInt) where T<:Base.BitSigned
     n = abs(x.size)
     if sizeof(T) < sizeof(Limb)
         SLimb = typeof(Signed(one(Limb)))
         convert(T, convert(SLimb, x))
     else
-        0 <= n <= cld(sizeof(T),sizeof(Limb)) || throw(InexactError(:convert, T, x))
+        0 <= n <= cld(sizeof(T),sizeof(Limb)) || throw(InexactError(Symbol(string(T)), T, x))
         y = x % T
-        ispos(x) ⊻ (y > 0) && throw(InexactError(:convert, T, x)) # catch overflow
+        ispos(x) ⊻ (y > 0) && throw(InexactError(Symbol(string(T)), T, x)) # catch overflow
         y
     end
 end
@@ -385,9 +385,9 @@ function (::Type{T})(n::BigInt, ::RoundingMode{:Nearest}) where T<:CdoubleMax
     x
 end
 
-convert(::Type{Float64}, n::BigInt) = Float64(n,RoundNearest)
-convert(::Type{Float32}, n::BigInt) = Float32(n,RoundNearest)
-convert(::Type{Float16}, n::BigInt) = Float16(n,RoundNearest)
+Float64(n::BigInt) = Float64(n, RoundNearest)
+Float32(n::BigInt) = Float32(n, RoundNearest)
+Float16(n::BigInt) = Float16(n, RoundNearest)
 
 promote_rule(::Type{BigInt}, ::Type{<:Integer}) = BigInt
 
diff --git a/base/inference.jl b/base/inference.jl
index f3925014d4808..01e02e7b94c3f 100644
--- a/base/inference.jl
+++ b/base/inference.jl
@@ -2086,7 +2086,13 @@ function abstract_call_method_with_const_args(@nospecialize(f), argtypes::Vector
     return result
 end
 
+const deprecated_sym = Symbol("deprecated.jl")
+
 function abstract_call_method(method::Method, @nospecialize(sig), sparams::SimpleVector, sv::InferenceState)
+    # TODO: remove with 0.7 deprecations
+    if method.file === deprecated_sym && method.sig == (Tuple{Type{T},Any} where T)
+        return Any, false
+    end
     topmost = nothing
     # Limit argument type tuple growth of functions:
     # look through the parents list to see if there's a call to the same method
@@ -2181,7 +2187,7 @@ function abstract_call_method(method::Method, @nospecialize(sig), sparams::Simpl
         recomputed = ccall(:jl_type_intersection_with_env, Any, (Any, Any), sig, method.sig)::SimpleVector
         sig = recomputed[1]
         if !isa(unwrap_unionall(sig), DataType) # probably Union{}
-            return Any
+            return Any, false
         end
         sparams = recomputed[2]::SimpleVector
     end
diff --git a/base/int.jl b/base/int.jl
index 4620784e3c3a8..554a0af63d68f 100644
--- a/base/int.jl
+++ b/base/int.jl
@@ -31,9 +31,6 @@ const BitUnsigned64T   = Union{Type{UInt8}, Type{UInt16}, Type{UInt32}, Type{UIn
 
 const BitIntegerType = Union{map(T->Type{T}, BitInteger_types)...}
 
-throw_inexacterror(f::Symbol, ::Type{T}, val) where T =
-    (@_noinline_meta; throw(InexactError(f, T, val)))
-
 ## integer comparisons ##
 
 (<)(x::T, y::T) where {T<:BitSigned}  = slt_int(x, y)
@@ -419,75 +416,19 @@ trailing_ones(x::Integer) = trailing_zeros(~x)
 >>>(x::BitInteger, y::Int) =
     select_value(0 <= y, x >>> unsigned(y), x << unsigned(-y))
 
-function is_top_bit_set(x::BitInteger)
-    @_inline_meta
-    lshr_int(x, (sizeof(x) << 0x03) - 1) == rem(0x01, typeof(x))
-end
-function check_top_bit(x::BitInteger)
-    @_inline_meta
-    is_top_bit_set(x) && throw_inexacterror(:check_top_bit, typeof(x), x)
-    x
-end
-
-## integer conversions ##
-
-function checked_trunc_sint(::Type{To}, x::From) where {To,From}
-    @_inline_meta
-    y = trunc_int(To, x)
-    back = sext_int(From, y)
-    x == back || throw_inexacterror(:trunc, To, x)
-    y
-end
-
-function checked_trunc_uint(::Type{To}, x::From) where {To,From}
-    @_inline_meta
-    y = trunc_int(To, x)
-    back = zext_int(From, y)
-    x == back || throw_inexacterror(:trunc, To, x)
-    y
-end
-
 for to in BitInteger_types, from in (BitInteger_types..., Bool)
     if !(to === from)
         if to.size < from.size
-            if to <: Signed
-                if from <: Unsigned
-                    @eval convert(::Type{$to}, x::($from)) =
-                        checked_trunc_sint($to, check_top_bit(x))
-                else
-                    @eval convert(::Type{$to}, x::($from)) =
-                        checked_trunc_sint($to, x)
-                end
-            else
-                @eval convert(::Type{$to}, x::($from)) =
-                    checked_trunc_uint($to, x)
-            end
             @eval rem(x::($from), ::Type{$to}) = trunc_int($to, x)
         elseif from === Bool
-            # Bools use i8 storage and may have garbage in their 7 high bits
-            @eval convert(::Type{$to}, x::($from)) = zext_int($to, x) & $to(1)
             @eval rem(x::($from), ::Type{$to}) = convert($to, x)
         elseif from.size < to.size
             if from <: Signed
-                if to <: Unsigned
-                    @eval convert(::Type{$to}, x::($from)) =
-                        sext_int($to, check_top_bit(x))
-                else
-                    @eval convert(::Type{$to}, x::($from)) =
-                        sext_int($to, x)
-                end
                 @eval rem(x::($from), ::Type{$to}) = sext_int($to, x)
             else
-                @eval convert(::Type{$to}, x::($from)) = zext_int($to, x)
                 @eval rem(x::($from), ::Type{$to}) = convert($to, x)
             end
         else
-            if !((from <: Signed) === (to <: Signed))
-                # raise InexactError if x's top bit is set
-                @eval convert(::Type{$to}, x::($from)) = bitcast($to, check_top_bit(x))
-            else
-                @eval convert(::Type{$to}, x::($from)) = bitcast($to, x)
-            end
             @eval rem(x::($from), ::Type{$to}) = bitcast($to, x)
         end
     end
@@ -522,16 +463,6 @@ rem(x::Integer, ::Type{Bool}) = ((x & 1) != 0)
 mod(x::Integer, ::Type{T}) where {T<:Integer} = rem(x, T)
 
 unsafe_trunc(::Type{T}, x::Integer) where {T<:Integer} = rem(x, T)
-for (Ts, Tu) in ((Int8, UInt8), (Int16, UInt16), (Int32, UInt32), (Int64, UInt64), (Int128, UInt128))
-    @eval convert(::Type{Signed}, x::$Tu) = convert($Ts, x)
-    @eval convert(::Type{Unsigned}, x::$Ts) = convert($Tu, x)
-end
-
-convert(::Type{Signed}, x::Union{Float32, Float64, Bool}) = convert(Int, x)
-convert(::Type{Unsigned}, x::Union{Float32, Float64, Bool}) = convert(UInt, x)
-
-convert(::Type{Integer}, x::Integer) = x
-convert(::Type{Integer}, x::Real) = convert(Signed, x)
 
 """
     trunc([T,] x, [digits, [base]])
diff --git a/base/irrationals.jl b/base/irrationals.jl
index 7a1509a2ff01f..4f55783514fe1 100644
--- a/base/irrationals.jl
+++ b/base/irrationals.jl
@@ -24,11 +24,11 @@ promote_rule(::Type{<:AbstractIrrational}, ::Type{Float32}) = Float32
 promote_rule(::Type{<:AbstractIrrational}, ::Type{<:AbstractIrrational}) = Float64
 promote_rule(::Type{<:AbstractIrrational}, ::Type{T}) where {T<:Number} = promote_type(Float64, T)
 
-convert(::Type{AbstractFloat}, x::AbstractIrrational) = Float64(x)
-convert(::Type{Float16}, x::AbstractIrrational) = Float16(Float32(x))
-convert(::Type{Complex{T}}, x::AbstractIrrational) where {T<:Real} = convert(Complex{T}, convert(T,x))
+AbstractFloat(x::AbstractIrrational) = Float64(x)
+Float16(x::AbstractIrrational) = Float16(Float32(x))
+Complex{T}(x::AbstractIrrational) where {T<:Real} = Complex{T}(T(x))
 
-@pure function convert(::Type{Rational{T}}, x::AbstractIrrational) where T<:Integer
+@pure function Rational{T}(x::AbstractIrrational) where T<:Integer
     o = precision(BigFloat)
     p = 256
     while true
@@ -42,7 +42,7 @@ convert(::Type{Complex{T}}, x::AbstractIrrational) where {T<:Real} = convert(Com
         p += 32
     end
 end
-convert(::Type{Rational{BigInt}}, x::AbstractIrrational) = throw(ArgumentError("Cannot convert an AbstractIrrational to a Rational{BigInt}: use rationalize(Rational{BigInt}, x) instead"))
+(::Type{Rational{BigInt}})(x::AbstractIrrational) = throw(ArgumentError("Cannot convert an AbstractIrrational to a Rational{BigInt}: use rationalize(Rational{BigInt}, x) instead"))
 
 @pure function (t::Type{T})(x::AbstractIrrational, r::RoundingMode) where T<:Union{Float32,Float64}
     setprecision(BigFloat, 256) do
@@ -126,27 +126,27 @@ macro irrational(sym, val, def)
     esym = esc(sym)
     qsym = esc(Expr(:quote, sym))
     bigconvert = isa(def,Symbol) ? quote
-        function Base.convert(::Type{BigFloat}, ::Irrational{$qsym})
+        function Base.BigFloat(::Irrational{$qsym})
             c = BigFloat()
             ccall(($(string("mpfr_const_", def)), :libmpfr),
                   Cint, (Ref{BigFloat}, Int32), c, MPFR.ROUNDING_MODE[])
             return c
         end
     end : quote
-        Base.convert(::Type{BigFloat}, ::Irrational{$qsym}) = $(esc(def))
+        Base.BigFloat(::Irrational{$qsym}) = $(esc(def))
     end
     quote
         const $esym = Irrational{$qsym}()
         $bigconvert
-        Base.convert(::Type{Float64}, ::Irrational{$qsym}) = $val
-        Base.convert(::Type{Float32}, ::Irrational{$qsym}) = $(Float32(val))
+        Base.Float64(::Irrational{$qsym}) = $val
+        Base.Float32(::Irrational{$qsym}) = $(Float32(val))
         @assert isa(big($esym), BigFloat)
         @assert Float64($esym) == Float64(big($esym))
         @assert Float32($esym) == Float32(big($esym))
     end
 end
 
-big(x::AbstractIrrational) = convert(BigFloat,x)
+big(x::AbstractIrrational) = BigFloat(x)
 big(::Type{<:AbstractIrrational}) = BigFloat
 
 # align along = for nice Array printing
diff --git a/base/libc.jl b/base/libc.jl
index fd7e5858a3fc9..cbe3323c2ef23 100644
--- a/base/libc.jl
+++ b/base/libc.jl
@@ -83,7 +83,6 @@ end
 
 Base.unsafe_convert(T::Union{Type{Ptr{Cvoid}},Type{Ptr{FILE}}}, f::FILE) = convert(T, f.ptr)
 Base.close(f::FILE) = systemerror("fclose", ccall(:fclose, Cint, (Ptr{Cvoid},), f.ptr) != 0)
-Base.convert(::Type{FILE}, s::IO) = FILE(s)
 
 function Base.seek(h::FILE, offset::Integer)
     systemerror("fseek", ccall(:fseek, Cint, (Ptr{Cvoid}, Clong, Cint),
diff --git a/base/libgit2/error.jl b/base/libgit2/error.jl
index 2f5739e0af879..b64e9f1b8d923 100644
--- a/base/libgit2/error.jl
+++ b/base/libgit2/error.jl
@@ -74,17 +74,17 @@ function last_error()
     err = ccall((:giterr_last, :libgit2), Ptr{ErrorStruct}, ())
     if err != C_NULL
         err_obj   = unsafe_load(err)
-        err_class = Class[err_obj.class][]
+        err_class = Class(err_obj.class)
         err_msg   = unsafe_string(err_obj.message)
     else
-        err_class = Class[0][]
+        err_class = Class(0)
         err_msg = "No errors"
     end
     return (err_class, err_msg)
 end
 
 function GitError(code::Integer)
-    err_code = Code[code][]
+    err_code = Code(code)
     err_class, err_msg = last_error()
     return GitError(err_class, err_code, err_msg)
 end
@@ -93,8 +93,7 @@ end # Error module
 
 macro check(git_func)
     quote
-        local err::Cint
-        err = $(esc(git_func::Expr))
+        err = Cint($(esc(git_func::Expr)))
         if err < 0
             throw(Error.GitError(err))
         end
diff --git a/base/libgit2/types.jl b/base/libgit2/types.jl
index 3bc83ade4a47d..30cc7fdcf068a 100644
--- a/base/libgit2/types.jl
+++ b/base/libgit2/types.jl
@@ -20,6 +20,7 @@ struct GitHash <: AbstractGitHash
     GitHash(val::NTuple{OID_RAWSZ, UInt8}) = new(val)
 end
 GitHash() = GitHash(ntuple(i->zero(UInt8), OID_RAWSZ))
+GitHash(h::GitHash) = h
 
 """
     GitShortHash(hash::GitHash, len::Integer)
diff --git a/base/linalg/bidiag.jl b/base/linalg/bidiag.jl
index 15cb73809fb5e..7c6ad8b1bd2eb 100644
--- a/base/linalg/bidiag.jl
+++ b/base/linalg/bidiag.jl
@@ -93,6 +93,8 @@ function Bidiagonal(A::AbstractMatrix, uplo::Symbol)
     Bidiagonal(diag(A, 0), diag(A, uplo == :U ? 1 : -1), uplo)
 end
 
+Bidiagonal(A::Bidiagonal) = A
+
 function getindex(A::Bidiagonal{T}, i::Integer, j::Integer) where T
     if !((1 <= i <= size(A,2)) && (1 <= j <= size(A,2)))
         throw(BoundsError(A,(i,j)))
@@ -131,7 +133,7 @@ function Base.replace_in_print_matrix(A::Bidiagonal,i::Integer,j::Integer,s::Abs
 end
 
 #Converting from Bidiagonal to dense Matrix
-function convert(::Type{Matrix{T}}, A::Bidiagonal) where T
+function Matrix{T}(A::Bidiagonal) where T
     n = size(A, 1)
     B = zeros(T, n, n)
     for i = 1:n - 1
@@ -145,15 +147,14 @@ function convert(::Type{Matrix{T}}, A::Bidiagonal) where T
     B[n,n] = A.dv[n]
     return B
 end
-convert(::Type{Matrix}, A::Bidiagonal{T}) where {T} = convert(Matrix{T}, A)
-convert(::Type{Array}, A::Bidiagonal) = convert(Matrix, A)
+Matrix(A::Bidiagonal{T}) where {T} = Matrix{T}(A)
+Array(A::Bidiagonal) = Matrix(A)
 promote_rule(::Type{Matrix{T}}, ::Type{<:Bidiagonal{S}}) where {T,S} =
     @isdefined(T) && @isdefined(S) ? Matrix{promote_type(T,S)} : Matrix
 promote_rule(::Type{Matrix}, ::Type{<:Bidiagonal}) = Matrix
 
 #Converting from Bidiagonal to Tridiagonal
-Tridiagonal(M::Bidiagonal{T}) where {T} = convert(Tridiagonal{T}, M)
-function convert(::Type{Tridiagonal{T}}, A::Bidiagonal) where T
+function Tridiagonal{T}(A::Bidiagonal) where T
     dv = convert(AbstractVector{T}, A.dv)
     ev = convert(AbstractVector{T}, A.ev)
     z = fill!(similar(ev), zero(T))
@@ -164,12 +165,12 @@ promote_rule(::Type{<:Tridiagonal{T}}, ::Type{<:Bidiagonal{S}}) where {T,S} =
 promote_rule(::Type{<:Tridiagonal}, ::Type{<:Bidiagonal}) = Tridiagonal
 
 # No-op for trivial conversion Bidiagonal{T} -> Bidiagonal{T}
-convert(::Type{Bidiagonal{T}}, A::Bidiagonal{T}) where {T} = A
+Bidiagonal{T}(A::Bidiagonal{T}) where {T} = A
 # Convert Bidiagonal to Bidiagonal{T} by constructing a new instance with converted elements
-convert(::Type{Bidiagonal{T}}, A::Bidiagonal) where {T} =
+Bidiagonal{T}(A::Bidiagonal) where {T} =
     Bidiagonal(convert(AbstractVector{T}, A.dv), convert(AbstractVector{T}, A.ev), A.uplo)
 # When asked to convert Bidiagonal to AbstractMatrix{T}, preserve structure by converting to Bidiagonal{T} <: AbstractMatrix{T}
-convert(::Type{AbstractMatrix{T}}, A::Bidiagonal) where {T} = convert(Bidiagonal{T}, A)
+AbstractMatrix{T}(A::Bidiagonal) where {T} = convert(Bidiagonal{T}, A)
 
 broadcast(::typeof(big), B::Bidiagonal) = Bidiagonal(big.(B.dv), big.(B.ev), B.uplo)
 
diff --git a/base/linalg/cholesky.jl b/base/linalg/cholesky.jl
index 3a8f1705e8914..8e1d338aa9781 100644
--- a/base/linalg/cholesky.jl
+++ b/base/linalg/cholesky.jl
@@ -349,30 +349,30 @@ function cholfact(x::Number, uplo::Symbol=:U)
 end
 
 
-function convert(::Type{Cholesky{T}}, C::Cholesky) where T
+function Cholesky{T}(C::Cholesky) where T
     Cnew = convert(AbstractMatrix{T}, C.factors)
     Cholesky{T, typeof(Cnew)}(Cnew, C.uplo, C.info)
 end
-convert(::Type{Factorization{T}}, C::Cholesky{T}) where {T} = C
-convert(::Type{Factorization{T}}, C::Cholesky) where {T} = convert(Cholesky{T}, C)
-convert(::Type{CholeskyPivoted{T}},C::CholeskyPivoted{T}) where {T} = C
-convert(::Type{CholeskyPivoted{T}},C::CholeskyPivoted) where {T} =
+Factorization{T}(C::Cholesky{T}) where {T} = C
+Factorization{T}(C::Cholesky) where {T} = Cholesky{T}(C)
+CholeskyPivoted{T}(C::CholeskyPivoted{T}) where {T} = C
+CholeskyPivoted{T}(C::CholeskyPivoted) where {T} =
     CholeskyPivoted(AbstractMatrix{T}(C.factors),C.uplo,C.piv,C.rank,C.tol,C.info)
-convert(::Type{Factorization{T}}, C::CholeskyPivoted{T}) where {T} = C
-convert(::Type{Factorization{T}}, C::CholeskyPivoted) where {T} = convert(CholeskyPivoted{T}, C)
+Factorization{T}(C::CholeskyPivoted{T}) where {T} = C
+Factorization{T}(C::CholeskyPivoted) where {T} = CholeskyPivoted{T}(C)
 
-convert(::Type{AbstractMatrix}, C::Cholesky) = C.uplo == 'U' ? C[:U]'C[:U] : C[:L]*C[:L]'
-convert(::Type{AbstractArray}, C::Cholesky) = convert(AbstractMatrix, C)
-convert(::Type{Matrix}, C::Cholesky) = convert(Array, convert(AbstractArray, C))
-convert(::Type{Array}, C::Cholesky) = convert(Matrix, C)
+AbstractMatrix(C::Cholesky) = C.uplo == 'U' ? C[:U]'C[:U] : C[:L]*C[:L]'
+AbstractArray(C::Cholesky) = AbstractMatrix(C)
+Matrix(C::Cholesky) = Array(AbstractArray(C))
+Array(C::Cholesky) = Matrix(C)
 
-function convert(::Type{AbstractMatrix}, F::CholeskyPivoted)
+function AbstractMatrix(F::CholeskyPivoted)
     ip = invperm(F[:p])
     (F[:L] * F[:U])[ip,ip]
 end
-convert(::Type{AbstractArray}, F::CholeskyPivoted) = convert(AbstractMatrix, F)
-convert(::Type{Matrix}, F::CholeskyPivoted) = convert(Array, convert(AbstractArray, F))
-convert(::Type{Array}, F::CholeskyPivoted) = convert(Matrix, F)
+AbstractArray(F::CholeskyPivoted) = AbstractMatrix(F)
+Matrix(F::CholeskyPivoted) = Array(AbstractArray(F))
+Array(F::CholeskyPivoted) = Matrix(F)
 
 copy(C::Cholesky) = Cholesky(copy(C.factors), C.uplo, C.info)
 copy(C::CholeskyPivoted) = CholeskyPivoted(copy(C.factors), C.uplo, C.piv, C.rank, C.tol, C.info)
diff --git a/base/linalg/diagonal.jl b/base/linalg/diagonal.jl
index a1190103df936..e2624f487e88b 100644
--- a/base/linalg/diagonal.jl
+++ b/base/linalg/diagonal.jl
@@ -49,11 +49,11 @@ Diagonal(V::AbstractVector{T}) where {T} = Diagonal{T,typeof(V)}(V)
 Diagonal{T}(V::AbstractVector{T}) where {T} = Diagonal{T,typeof(V)}(V)
 Diagonal{T}(V::AbstractVector) where {T} = Diagonal{T}(convert(AbstractVector{T}, V))
 
-convert(::Type{Diagonal{T}}, D::Diagonal{T}) where {T} = D
-convert(::Type{Diagonal{T}}, D::Diagonal) where {T} = Diagonal{T}(convert(AbstractVector{T}, D.diag))
-convert(::Type{AbstractMatrix{T}}, D::Diagonal) where {T} = convert(Diagonal{T}, D)
-convert(::Type{Matrix}, D::Diagonal) = diagm(0 => D.diag)
-convert(::Type{Array}, D::Diagonal) = convert(Matrix, D)
+Diagonal{T}(D::Diagonal{T}) where {T} = D
+Diagonal{T}(D::Diagonal) where {T} = Diagonal{T}(convert(AbstractVector{T}, D.diag))
+AbstractMatrix{T}(D::Diagonal) where {T} = Diagonal{T}(D)
+Matrix(D::Diagonal) = diagm(0 => D.diag)
+Array(D::Diagonal) = Matrix(D)
 
 # For D<:Diagonal, similar(D[, neweltype]) should yield a Diagonal matrix.
 # On the other hand, similar(D, [neweltype,] shape...) should yield a sparse matrix.
diff --git a/base/linalg/eigen.jl b/base/linalg/eigen.jl
index 2c92c9fa4ba55..d30fae6e6080b 100644
--- a/base/linalg/eigen.jl
+++ b/base/linalg/eigen.jl
@@ -526,7 +526,7 @@ eigvecs(A::AbstractMatrix, B::AbstractMatrix) = eigvecs(eigfact(A, B))
 # Conversion methods
 
 ## Can we determine the source/result is Real?  This is not stored in the type Eigen
-convert(::Type{AbstractMatrix}, F::Eigen) = F.vectors * Diagonal(F.values) / F.vectors
-convert(::Type{AbstractArray}, F::Eigen) = convert(AbstractMatrix, F)
-convert(::Type{Matrix}, F::Eigen) = convert(Array, convert(AbstractArray, F))
-convert(::Type{Array}, F::Eigen) = convert(Matrix, F)
+AbstractMatrix(F::Eigen) = F.vectors * Diagonal(F.values) / F.vectors
+AbstractArray(F::Eigen) = AbstractMatrix(F)
+Matrix(F::Eigen) = Array(AbstractArray(F))
+Array(F::Eigen) = Matrix(F)
diff --git a/base/linalg/factorization.jl b/base/linalg/factorization.jl
index 1eedc04270415..3bef6499d1bb9 100644
--- a/base/linalg/factorization.jl
+++ b/base/linalg/factorization.jl
@@ -45,8 +45,13 @@ function det(F::Factorization)
     return exp(d)*s
 end
 
+convert(::Type{T}, f::T) where {T<:Factorization} = f
+convert(::Type{T}, f::Factorization) where {T<:Factorization} = T(f)
+
+convert(::Type{T}, f::Factorization) where {T<:AbstractArray} = T(f)
+
 ### General promotion rules
-convert(::Type{Factorization{T}}, F::Factorization{T}) where {T} = F
+Factorization{T}(F::Factorization{T}) where {T} = F
 inv(F::Factorization{T}) where {T} = (n = size(F, 1); ldiv!(F, Matrix{T}(I, n, n)))
 
 Base.hash(F::Factorization, h::UInt) = mapreduce(f -> hash(getfield(F, f)), hash, h, 1:nfields(F))
diff --git a/base/linalg/givens.jl b/base/linalg/givens.jl
index 539f5694351d9..daa3cebb0416d 100644
--- a/base/linalg/givens.jl
+++ b/base/linalg/givens.jl
@@ -37,12 +37,15 @@ mutable struct Rotation{T} <: AbstractRotation{T}
     rotations::Vector{Givens{T}}
 end
 
-convert(::Type{Givens{T}}, G::Givens{T}) where {T} = G
-convert(::Type{Givens{T}}, G::Givens) where {T} = Givens(G.i1, G.i2, convert(T, G.c), convert(T, G.s))
-convert(::Type{Rotation{T}}, R::Rotation{T}) where {T} = R
-convert(::Type{Rotation{T}}, R::Rotation) where {T} = Rotation{T}([convert(Givens{T}, g) for g in R.rotations])
-convert(::Type{AbstractRotation{T}}, G::Givens) where {T} = convert(Givens{T}, G)
-convert(::Type{AbstractRotation{T}}, R::Rotation) where {T} = convert(Rotation{T}, R)
+convert(::Type{T}, r::T) where {T<:AbstractRotation} = r
+convert(::Type{T}, r::AbstractRotation) where {T<:AbstractRotation} = T(r)
+
+Givens{T}(G::Givens{T}) where {T} = G
+Givens{T}(G::Givens) where {T} = Givens(G.i1, G.i2, convert(T, G.c), convert(T, G.s))
+Rotation{T}(R::Rotation{T}) where {T} = R
+Rotation{T}(R::Rotation) where {T} = Rotation{T}([Givens{T}(g) for g in R.rotations])
+AbstractRotation{T}(G::Givens) where {T} = Givens{T}(G)
+AbstractRotation{T}(R::Rotation) where {T} = Rotation{T}(R)
 
 adjoint(G::Givens) = Givens(G.i1, G.i2, conj(G.c), -G.s)
 adjoint(R::Rotation{T}) where {T} = Rotation{T}(reverse!([adjoint(r) for r in R.rotations]))
diff --git a/base/linalg/hessenberg.jl b/base/linalg/hessenberg.jl
index 1d13fb7eb591f..6c253b3aff39d 100644
--- a/base/linalg/hessenberg.jl
+++ b/base/linalg/hessenberg.jl
@@ -75,12 +75,12 @@ function getindex(A::HessenbergQ, i::Integer, j::Integer)
 end
 
 ## reconstruct the original matrix
-convert(::Type{Matrix}, A::HessenbergQ{<:BlasFloat}) = LAPACK.orghr!(1, size(A.factors, 1), copy(A.factors), A.τ)
-convert(::Type{Array}, A::HessenbergQ) = convert(Matrix, A)
-convert(::Type{AbstractMatrix}, F::Hessenberg) = (fq = Array(F[:Q]); (fq * F[:H]) * fq')
-convert(::Type{AbstractArray}, F::Hessenberg) = convert(AbstractMatrix, F)
-convert(::Type{Matrix}, F::Hessenberg) = convert(Array, convert(AbstractArray, F))
-convert(::Type{Array}, F::Hessenberg) = convert(Matrix, F)
+Matrix(A::HessenbergQ{<:BlasFloat}) = LAPACK.orghr!(1, size(A.factors, 1), copy(A.factors), A.τ)
+Array(A::HessenbergQ) = Matrix(A)
+AbstractMatrix(F::Hessenberg) = (fq = Array(F[:Q]); (fq * F[:H]) * fq')
+AbstractArray(F::Hessenberg) = AbstractMatrix(F)
+Matrix(F::Hessenberg) = Array(AbstractArray(F))
+Array(F::Hessenberg) = Matrix(F)
 
 mul!(Q::HessenbergQ{T}, X::StridedVecOrMat{T}) where {T<:BlasFloat} =
     LAPACK.ormhr!('L', 'N', 1, size(Q.factors, 1), Q.factors, Q.τ, X)
diff --git a/base/linalg/ldlt.jl b/base/linalg/ldlt.jl
index d8bc1f38c979a..7db241411102f 100644
--- a/base/linalg/ldlt.jl
+++ b/base/linalg/ldlt.jl
@@ -7,13 +7,13 @@ end
 size(S::LDLt) = size(S.data)
 size(S::LDLt, i::Integer) = size(S.data, i)
 
-convert(::Type{LDLt{T,S}}, F::LDLt) where {T,S} = LDLt{T,S}(convert(S, F.data))
+LDLt{T,S}(F::LDLt) where {T,S<:AbstractMatrix} = LDLt{T,S}(convert(S, F.data))
 # NOTE: the annotaion <:AbstractMatrix shouldn't be necessary, it is introduced
 #       to avoid an ambiguity warning (see issue #6383)
-convert(::Type{LDLt{T}}, F::LDLt{S,U}) where {T,S,U<:AbstractMatrix} = convert(LDLt{T,U}, F)
+LDLt{T}(F::LDLt{S,U}) where {T,S,U<:AbstractMatrix} = LDLt{T,U}(F)
 
-convert(::Type{Factorization{T}}, F::LDLt{T}) where {T} = F
-convert(::Type{Factorization{T}}, F::LDLt{S,U}) where {T,S,U} = convert(LDLt{T,U}, F)
+Factorization{T}(F::LDLt{T}) where {T} = F
+Factorization{T}(F::LDLt{S,U}) where {T,S,U} = LDLt{T,U}(F)
 
 # SymTridiagonal
 """
@@ -86,7 +86,7 @@ julia> S \\ b
 """
 function ldltfact(M::SymTridiagonal{T}) where T
     S = typeof(zero(T)/one(T))
-    return S == T ? ldltfact!(copy(M)) : ldltfact!(convert(SymTridiagonal{S}, M))
+    return S == T ? ldltfact!(copy(M)) : ldltfact!(SymTridiagonal{S}(M))
 end
 
 factorize(S::SymTridiagonal) = ldltfact(S)
@@ -127,14 +127,14 @@ function logabsdet(F::LDLt{<:Any,<:SymTridiagonal})
 end
 
 # Conversion methods
-function convert(::Type{SymTridiagonal}, F::LDLt)
+function SymTridiagonal(F::LDLt)
     e = copy(F.data.ev)
     d = copy(F.data.dv)
     e .*= d[1:end-1]
     d[2:end] += e .* F.data.ev
     SymTridiagonal(d, e)
 end
-convert(::Type{AbstractMatrix}, F::LDLt) = convert(SymTridiagonal, F)
-convert(::Type{AbstractArray}, F::LDLt) = convert(AbstractMatrix, F)
-convert(::Type{Matrix}, F::LDLt) = convert(Array, convert(AbstractArray, F))
-convert(::Type{Array}, F::LDLt) = convert(Matrix, F)
+AbstractMatrix(F::LDLt) = SymTridiagonal(F)
+AbstractArray(F::LDLt) = AbstractMatrix(F)
+Matrix(F::LDLt) = Array(AbstractArray(F))
+Array(F::LDLt) = Matrix(F)
diff --git a/base/linalg/lq.jl b/base/linalg/lq.jl
index d4424900dbd9a..e91f0cfea2947 100644
--- a/base/linalg/lq.jl
+++ b/base/linalg/lq.jl
@@ -62,13 +62,13 @@ end
 
 copy(A::LQ) = LQ(copy(A.factors), copy(A.τ))
 
-convert(::Type{LQ{T}},A::LQ) where {T} = LQ(convert(AbstractMatrix{T}, A.factors), convert(Vector{T}, A.τ))
-convert(::Type{Factorization{T}}, A::LQ{T}) where {T} = A
-convert(::Type{Factorization{T}}, A::LQ) where {T} = convert(LQ{T}, A)
-convert(::Type{AbstractMatrix}, A::LQ) = A[:L]*A[:Q]
-convert(::Type{AbstractArray}, A::LQ) = convert(AbstractMatrix, A)
-convert(::Type{Matrix}, A::LQ) = convert(Array, convert(AbstractArray, A))
-convert(::Type{Array}, A::LQ) = convert(Matrix, A)
+LQ{T}(A::LQ) where {T} = LQ(convert(AbstractMatrix{T}, A.factors), convert(Vector{T}, A.τ))
+Factorization{T}(A::LQ{T}) where {T} = A
+Factorization{T}(A::LQ) where {T} = LQ{T}(A)
+AbstractMatrix(A::LQ) = A[:L]*A[:Q]
+AbstractArray(A::LQ) = AbstractMatrix(A)
+Matrix(A::LQ) = Array(AbstractArray(A))
+Array(A::LQ) = Matrix(A)
 
 adjoint(A::LQ{T}) where {T} = QR{T,typeof(A.factors)}(adjoint(A.factors), A.τ)
 
@@ -95,10 +95,10 @@ function show(io::IO, C::LQ)
     show(io, C[:Q])
 end
 
-convert(::Type{LQPackedQ{T}}, Q::LQPackedQ) where {T} = LQPackedQ(convert(AbstractMatrix{T}, Q.factors), convert(Vector{T}, Q.τ))
-convert(::Type{AbstractMatrix{T}}, Q::LQPackedQ) where {T} = convert(LQPackedQ{T}, Q)
-convert(::Type{Matrix}, A::LQPackedQ) = LAPACK.orglq!(copy(A.factors),A.τ)
-convert(::Type{Array}, A::LQPackedQ) = convert(Matrix, A)
+LQPackedQ{T}(Q::LQPackedQ) where {T} = LQPackedQ(convert(AbstractMatrix{T}, Q.factors), convert(Vector{T}, Q.τ))
+AbstractMatrix{T}(Q::LQPackedQ) where {T} = LQPackedQ{T}(Q)
+Matrix(A::LQPackedQ) = LAPACK.orglq!(copy(A.factors),A.τ)
+Array(A::LQPackedQ) = Matrix(A)
 
 size(A::LQ, dim::Integer) = size(A.factors, dim)
 size(A::LQ) = size(A.factors)
@@ -128,15 +128,15 @@ mul!(A::QR{T}, B::LQ{T}) where {T<:BlasFloat} =
     mul!(zeros(eltype(A), size(A)), Matrix(A), Matrix(B))
 function *(A::LQ{TA}, B::StridedVecOrMat{TB}) where {TA,TB}
     TAB = promote_type(TA, TB)
-    mul!(convert(Factorization{TAB},A), copy_oftype(B, TAB))
+    mul!(Factorization{TAB}(A), copy_oftype(B, TAB))
 end
 function *(A::LQ{TA},B::QR{TB}) where {TA,TB}
     TAB = promote_type(TA, TB)
-    mul!(convert(Factorization{TAB},A), convert(Factorization{TAB},B))
+    mul!(Factorization{TAB}(A), Factorization{TAB}(B))
 end
 function *(A::QR{TA},B::LQ{TB}) where {TA,TB}
     TAB = promote_type(TA, TB)
-    mul!(convert(Factorization{TAB},A), convert(Factorization{TAB},B))
+    mul!(Factorization{TAB}(A), Factorization{TAB}(B))
 end
 *(A::Adjoint{<:Any,<:LQ}, B::LQ) = adjoint(A.parent) * B
 *(A::LQ, B::Adjoint{<:Any,<:LQ}) = A * adjoint(B.parent)
@@ -146,7 +146,7 @@ end
 mul!(A::LQPackedQ{T}, B::StridedVecOrMat{T}) where {T<:BlasFloat} = LAPACK.ormlq!('L','N',A.factors,A.τ,B)
 function (*)(A::LQPackedQ, B::StridedVecOrMat)
     TAB = promote_type(eltype(A), eltype(B))
-    mul!(convert(AbstractMatrix{TAB}, A), copy_oftype(B, TAB))
+    mul!(AbstractMatrix{TAB}(A), copy_oftype(B, TAB))
 end
 
 ### QcB
@@ -158,9 +158,9 @@ function *(adjA::Adjoint{<:Any,<:LQPackedQ}, B::StridedVecOrMat)
     A = adjA.parent
     TAB = promote_type(eltype(A), eltype(B))
     if size(B,1) == size(A.factors,2)
-        mul!(Adjoint(convert(AbstractMatrix{TAB}, A)), copy_oftype(B, TAB))
+        mul!(Adjoint(AbstractMatrix{TAB}(A)), copy_oftype(B, TAB))
     elseif size(B,1) == size(A.factors,1)
-        mul!(Adjoint(convert(AbstractMatrix{TAB}, A)), [B; zeros(TAB, size(A.factors, 2) - size(A.factors, 1), size(B, 2))])
+        mul!(Adjoint(AbstractMatrix{TAB}(A)), [B; zeros(TAB, size(A.factors, 2) - size(A.factors, 1), size(B, 2))])
     else
         throw(DimensionMismatch("first dimension of B, $(size(B,1)), must equal one of the dimensions of A, $(size(A))"))
     end
@@ -209,13 +209,13 @@ mul!(A::StridedMatrix{T}, adjB::Adjoint{<:Any,<:LQPackedQ{T}}) where {T<:BlasCom
 function *(A::StridedVecOrMat, adjQ::Adjoint{<:Any,<:LQPackedQ})
     Q = adjQ.parent
     TR = promote_type(eltype(A), eltype(Q))
-    return mul!(copy_oftype(A, TR), Adjoint(convert(AbstractMatrix{TR}, Q)))
+    return mul!(copy_oftype(A, TR), Adjoint(AbstractMatrix{TR}(Q)))
 end
 function *(adjA::Adjoint{<:Any,<:StridedMatrix}, adjQ::Adjoint{<:Any,<:LQPackedQ})
     A, Q = adjA.parent, adjQ.parent
     TR = promote_type(eltype(A), eltype(Q))
     C = adjoint!(similar(A, TR, reverse(size(A))), A)
-    return mul!(C, Adjoint(convert(AbstractMatrix{TR}, Q)))
+    return mul!(C, Adjoint(AbstractMatrix{TR}(Q)))
 end
 #
 # (2) the inner dimension in the multiplication is the LQPackedQ's first dimension.
@@ -240,7 +240,7 @@ function *(A::StridedVecOrMat, Q::LQPackedQ)
     else
         _rightappdimmismatch("columns")
     end
-    return mul!(C, convert(AbstractMatrix{TR}, Q))
+    return mul!(C, AbstractMatrix{TR}(Q))
 end
 function *(adjA::Adjoint{<:Any,<:StridedMatrix}, Q::LQPackedQ)
     A = adjA.parent
@@ -253,7 +253,7 @@ function *(adjA::Adjoint{<:Any,<:StridedMatrix}, Q::LQPackedQ)
     else
         _rightappdimmismatch("rows")
     end
-    return mul!(C, convert(AbstractMatrix{TR}, Q))
+    return mul!(C, AbstractMatrix{TR}(Q))
 end
 _rightappdimmismatch(rowsorcols) =
     throw(DimensionMismatch(string("the number of $(rowsorcols) of the matrix on the left ",
@@ -266,7 +266,7 @@ function (\)(A::LQ{TA}, b::StridedVector{Tb}) where {TA,Tb}
     S = promote_type(TA,Tb)
     m = checksquare(A)
     m == length(b) || throw(DimensionMismatch("left hand side has $m rows, but right hand side has length $(length(b))"))
-    AA = convert(Factorization{S}, A)
+    AA = Factorization{S}(A)
     x = ldiv!(AA, copy_oftype(b, S))
     return x
 end
@@ -274,7 +274,7 @@ function (\)(A::LQ{TA},B::StridedMatrix{TB}) where {TA,TB}
     S = promote_type(TA,TB)
     m = checksquare(A)
     m == size(B,1) || throw(DimensionMismatch("left hand side has $m rows, but right hand side has $(size(B,1)) rows"))
-    AA = convert(Factorization{S}, A)
+    AA = Factorization{S}(A)
     X = ldiv!(AA, copy_oftype(B, S))
     return X
 end
diff --git a/base/linalg/lu.jl b/base/linalg/lu.jl
index d8ca0dae38494..838b46d1552ef 100644
--- a/base/linalg/lu.jl
+++ b/base/linalg/lu.jl
@@ -227,13 +227,13 @@ function lu(A::AbstractMatrix, pivot::Union{Val{false}, Val{true}} = Val(true))
     F[:L], F[:U], F[:p]
 end
 
-function convert(::Type{LU{T}}, F::LU) where T
+function LU{T}(F::LU) where T
     M = convert(AbstractMatrix{T}, F.factors)
     LU{T,typeof(M)}(M, F.ipiv, F.info)
 end
-convert(::Type{LU{T,S}}, F::LU) where {T,S} = LU{T,S}(convert(S, F.factors), F.ipiv, F.info)
-convert(::Type{Factorization{T}}, F::LU{T}) where {T} = F
-convert(::Type{Factorization{T}}, F::LU) where {T} = convert(LU{T}, F)
+LU{T,S}(F::LU) where {T,S} = LU{T,S}(convert(S, F.factors), F.ipiv, F.info)
+Factorization{T}(F::LU{T}) where {T} = F
+Factorization{T}(F::LU) where {T} = LU{T}(F)
 
 copy(A::LU{T,S}) where {T,S} = LU{T,S}(copy(A.factors), copy(A.ipiv), A.info)
 
@@ -593,12 +593,12 @@ end
 /(B::AbstractMatrix,A::LU) = transpose(Transpose(A) \ Transpose(B))
 
 # Conversions
-convert(::Type{AbstractMatrix}, F::LU) = (F[:L] * F[:U])[invperm(F[:p]),:]
-convert(::Type{AbstractArray}, F::LU) = convert(AbstractMatrix, F)
-convert(::Type{Matrix}, F::LU) = convert(Array, convert(AbstractArray, F))
-convert(::Type{Array}, F::LU) = convert(Matrix, F)
+AbstractMatrix(F::LU) = (F[:L] * F[:U])[invperm(F[:p]),:]
+AbstractArray(F::LU) = AbstractMatrix(F)
+Matrix(F::LU) = Array(AbstractArray(F))
+Array(F::LU) = Matrix(F)
 
-function convert(::Type{Tridiagonal}, F::Base.LinAlg.LU{T,Tridiagonal{T,V}}) where {T,V}
+function Tridiagonal(F::Base.LinAlg.LU{T,Tridiagonal{T,V}}) where {T,V}
     n = size(F, 1)
 
     dl  = copy(F.factors.dl)
@@ -632,11 +632,7 @@ function convert(::Type{Tridiagonal}, F::Base.LinAlg.LU{T,Tridiagonal{T,V}}) whe
     end
     return Tridiagonal(dl, d, du)
 end
-convert(::Type{AbstractMatrix}, F::LU{T,Tridiagonal{T,V}}) where {T,V} =
-    convert(Tridiagonal, F)
-convert(::Type{AbstractArray}, F::LU{T,Tridiagonal{T,V}}) where {T,V} =
-    convert(AbstractMatrix, F)
-convert(::Type{Matrix}, F::LU{T,Tridiagonal{T,V}}) where {T,V} =
-    convert(Array, convert(AbstractArray, F))
-convert(::Type{Array}, F::LU{T,Tridiagonal{T,V}}) where {T,V} =
-    convert(Matrix, F)
+AbstractMatrix(F::LU{T,Tridiagonal{T,V}}) where {T,V} = Tridiagonal(F)
+AbstractArray(F::LU{T,Tridiagonal{T,V}}) where {T,V} = AbstractMatrix(F)
+Matrix(F::LU{T,Tridiagonal{T,V}}) where {T,V} = Array(AbstractArray(F))
+Array(F::LU{T,Tridiagonal{T,V}}) where {T,V} = Matrix(F)
diff --git a/base/linalg/qr.jl b/base/linalg/qr.jl
index 435f2a67ac12e..9c2f0c0ee76fc 100644
--- a/base/linalg/qr.jl
+++ b/base/linalg/qr.jl
@@ -404,23 +404,23 @@ function qr!(v::AbstractVector)
 end
 
 # Conversions
-convert(::Type{QR{T}}, A::QR) where {T} = QR(convert(AbstractMatrix{T}, A.factors), convert(Vector{T}, A.τ))
-convert(::Type{Factorization{T}}, A::QR{T}) where {T} = A
-convert(::Type{Factorization{T}}, A::QR) where {T} = convert(QR{T}, A)
-convert(::Type{QRCompactWY{T}}, A::QRCompactWY) where {T} = QRCompactWY(convert(AbstractMatrix{T}, A.factors), convert(AbstractMatrix{T}, A.T))
-convert(::Type{Factorization{T}}, A::QRCompactWY{T}) where {T} = A
-convert(::Type{Factorization{T}}, A::QRCompactWY) where {T} = convert(QRCompactWY{T}, A)
-convert(::Type{AbstractMatrix}, F::Union{QR,QRCompactWY}) = F[:Q] * F[:R]
-convert(::Type{AbstractArray}, F::Union{QR,QRCompactWY}) = convert(AbstractMatrix, F)
-convert(::Type{Matrix}, F::Union{QR,QRCompactWY}) = convert(Array, convert(AbstractArray, F))
-convert(::Type{Array}, F::Union{QR,QRCompactWY}) = convert(Matrix, F)
-convert(::Type{QRPivoted{T}}, A::QRPivoted) where {T} = QRPivoted(convert(AbstractMatrix{T}, A.factors), convert(Vector{T}, A.τ), A.jpvt)
-convert(::Type{Factorization{T}}, A::QRPivoted{T}) where {T} = A
-convert(::Type{Factorization{T}}, A::QRPivoted) where {T} = convert(QRPivoted{T}, A)
-convert(::Type{AbstractMatrix}, F::QRPivoted) = (F[:Q] * F[:R])[:,invperm(F[:p])]
-convert(::Type{AbstractArray}, F::QRPivoted) = convert(AbstractMatrix, F)
-convert(::Type{Matrix}, F::QRPivoted) = convert(Array, convert(AbstractArray, F))
-convert(::Type{Array}, F::QRPivoted) = convert(Matrix, F)
+QR{T}(A::QR) where {T} = QR(convert(AbstractMatrix{T}, A.factors), convert(Vector{T}, A.τ))
+Factorization{T}(A::QR{T}) where {T} = A
+Factorization{T}(A::QR) where {T} = QR{T}(A)
+QRCompactWY{T}(A::QRCompactWY) where {T} = QRCompactWY(convert(AbstractMatrix{T}, A.factors), convert(AbstractMatrix{T}, A.T))
+Factorization{T}(A::QRCompactWY{T}) where {T} = A
+Factorization{T}(A::QRCompactWY) where {T} = QRCompactWY{T}(A)
+AbstractMatrix(F::Union{QR,QRCompactWY}) = F[:Q] * F[:R]
+AbstractArray(F::Union{QR,QRCompactWY}) = AbstractMatrix(F)
+Matrix(F::Union{QR,QRCompactWY}) = Array(AbstractArray(F))
+Array(F::Union{QR,QRCompactWY}) = Matrix(F)
+QRPivoted{T}(A::QRPivoted) where {T} = QRPivoted(convert(AbstractMatrix{T}, A.factors), convert(Vector{T}, A.τ), A.jpvt)
+Factorization{T}(A::QRPivoted{T}) where {T} = A
+Factorization{T}(A::QRPivoted) where {T} = QRPivoted{T}(A)
+AbstractMatrix(F::QRPivoted) = (F[:Q] * F[:R])[:,invperm(F[:p])]
+AbstractArray(F::QRPivoted) = AbstractMatrix(F)
+Matrix(F::QRPivoted) = Array(AbstractArray(F))
+Array(F::QRPivoted) = Matrix(F)
 
 function show(io::IO, F::Union{QR, QRCompactWY, QRPivoted})
     println(io, "$(typeof(F)) with factors Q and R:")
@@ -502,14 +502,14 @@ struct QRCompactWYQ{S, M<:AbstractMatrix} <: AbstractQ{S}
 end
 QRCompactWYQ(factors::AbstractMatrix{S}, T::Matrix{S}) where {S} = QRCompactWYQ{S,typeof(factors)}(factors, T)
 
-convert(::Type{QRPackedQ{T}}, Q::QRPackedQ) where {T} = QRPackedQ(convert(AbstractMatrix{T}, Q.factors), convert(Vector{T}, Q.τ))
-convert(::Type{AbstractMatrix{T}}, Q::QRPackedQ{T}) where {T} = Q
-convert(::Type{AbstractMatrix{T}}, Q::QRPackedQ) where {T} = convert(QRPackedQ{T}, Q)
-convert(::Type{QRCompactWYQ{S}}, Q::QRCompactWYQ) where {S} = QRCompactWYQ(convert(AbstractMatrix{S}, Q.factors), convert(AbstractMatrix{S}, Q.T))
-convert(::Type{AbstractMatrix{S}}, Q::QRCompactWYQ{S}) where {S} = Q
-convert(::Type{AbstractMatrix{S}}, Q::QRCompactWYQ) where {S} = convert(QRCompactWYQ{S}, Q)
-convert(::Type{Matrix}, A::AbstractQ{T}) where {T} = mul!(A, Matrix{T}(I, size(A.factors, 1), min(size(A.factors)...)))
-convert(::Type{Array}, A::AbstractQ) = convert(Matrix, A)
+QRPackedQ{T}(Q::QRPackedQ) where {T} = QRPackedQ(convert(AbstractMatrix{T}, Q.factors), convert(Vector{T}, Q.τ))
+AbstractMatrix{T}(Q::QRPackedQ{T}) where {T} = Q
+AbstractMatrix{T}(Q::QRPackedQ) where {T} = QRPackedQ{T}(Q)
+QRCompactWYQ{S}(Q::QRCompactWYQ) where {S} = QRCompactWYQ(convert(AbstractMatrix{S}, Q.factors), convert(AbstractMatrix{S}, Q.T))
+AbstractMatrix{S}(Q::QRCompactWYQ{S}) where {S} = Q
+AbstractMatrix{S}(Q::QRCompactWYQ) where {S} = QRCompactWYQ{S}(Q)
+Matrix(A::AbstractQ{T}) where {T} = mul!(A, Matrix{T}(I, size(A.factors, 1), min(size(A.factors)...)))
+Array(A::AbstractQ) = Matrix(A)
 
 size(A::Union{QR,QRCompactWY,QRPivoted}, dim::Integer) = size(A.factors, dim)
 size(A::Union{QR,QRCompactWY,QRPivoted}) = size(A.factors)
@@ -857,7 +857,7 @@ function (\)(A::Union{QR{TA},QRCompactWY{TA},QRPivoted{TA}}, B::AbstractVecOrMat
     m, n = size(A)
     m == size(B,1) || throw(DimensionMismatch("left hand side has $m rows, but right hand side has $(size(B,1)) rows"))
 
-    AA = convert(Factorization{S}, A)
+    AA = Factorization{S}(A)
 
     X = _zeros(S, B, n)
     X[1:size(B, 1), :] = B
diff --git a/base/linalg/rowvector.jl b/base/linalg/rowvector.jl
index 0ad9ca8a69a35..89170bc29fd72 100644
--- a/base/linalg/rowvector.jl
+++ b/base/linalg/rowvector.jl
@@ -84,7 +84,7 @@ const ConjRowVector{T,CV<:ConjVector} = RowVector{T,CV}
         error("RowVector expects 1×N size, got $n")
 
 # Conversion of underlying storage
-convert(::Type{RowVector{T,V}}, rowvec::RowVector) where {T,V<:AbstractVector} =
+RowVector{T,V}(rowvec::RowVector) where {T,V<:AbstractVector} =
     RowVector{T,V}(convert(V,rowvec.vec))
 
 # similar tries to maintain the RowVector wrapper and the parent type
diff --git a/base/linalg/schur.jl b/base/linalg/schur.jl
index 73fa0c5f6cf89..6458d45592e91 100644
--- a/base/linalg/schur.jl
+++ b/base/linalg/schur.jl
@@ -295,10 +295,10 @@ function schur(A::StridedMatrix, B::StridedMatrix)
 end
 
 # Conversion
-convert(::Type{AbstractMatrix}, F::Schur) = (F.Z * F.T) * F.Z'
-convert(::Type{AbstractArray}, F::Schur) = convert(AbstractMatrix, F)
-convert(::Type{Matrix}, F::Schur) = convert(Array, convert(AbstractArray, F))
-convert(::Type{Array}, F::Schur) = convert(Matrix, F)
+AbstractMatrix(F::Schur) = (F.Z * F.T) * F.Z'
+AbstractArray(F::Schur) = AbstractMatrix(F)
+Matrix(F::Schur) = Array(AbstractArray(F))
+Array(F::Schur) = Matrix(F)
 
 copy(F::Schur) = Schur(copy(F.T), copy(F.Z), copy(F.values))
 copy(F::GeneralizedSchur) = GeneralizedSchur(copy(F.S), copy(F.T), copy(F.alpha), copy(F.beta), copy(F.Q), copy(F.Z))
diff --git a/base/linalg/special.jl b/base/linalg/special.jl
index 364518507f04f..40d13824fbcbf 100644
--- a/base/linalg/special.jl
+++ b/base/linalg/special.jl
@@ -6,58 +6,54 @@
 # Interconversion between special matrix types
 
 # conversions from Diagonal to other special matrix types
-convert(::Type{Bidiagonal}, A::Diagonal) =
-    Bidiagonal(A.diag, fill!(similar(A.diag, length(A.diag)-1), 0), :U)
-convert(::Type{SymTridiagonal}, A::Diagonal) =
-    SymTridiagonal(A.diag, fill!(similar(A.diag, length(A.diag)-1), 0))
-convert(::Type{Tridiagonal}, A::Diagonal) =
-    Tridiagonal(fill!(similar(A.diag, length(A.diag)-1), 0), A.diag,
-                fill!(similar(A.diag, length(A.diag)-1), 0))
+Bidiagonal(A::Diagonal) = Bidiagonal(A.diag, fill!(similar(A.diag, length(A.diag)-1), 0), :U)
+SymTridiagonal(A::Diagonal) = SymTridiagonal(A.diag, fill!(similar(A.diag, length(A.diag)-1), 0))
+Tridiagonal(A::Diagonal) = Tridiagonal(fill!(similar(A.diag, length(A.diag)-1), 0), A.diag,
+                                       fill!(similar(A.diag, length(A.diag)-1), 0))
 
 # conversions from Bidiagonal to other special matrix types
-convert(::Type{Diagonal}, A::Bidiagonal) =
+Diagonal(A::Bidiagonal) =
     iszero(A.ev) ? Diagonal(A.dv) :
         throw(ArgumentError("matrix cannot be represented as Diagonal"))
-convert(::Type{SymTridiagonal}, A::Bidiagonal) =
+SymTridiagonal(A::Bidiagonal) =
     iszero(A.ev) ? SymTridiagonal(A.dv, A.ev) :
         throw(ArgumentError("matrix cannot be represented as SymTridiagonal"))
-convert(::Type{Tridiagonal}, A::Bidiagonal) =
+Tridiagonal(A::Bidiagonal) =
     Tridiagonal(A.uplo == 'U' ? fill!(similar(A.ev), 0) : A.ev, A.dv,
                 A.uplo == 'U' ? A.ev : fill!(similar(A.ev), 0))
 
 # conversions from SymTridiagonal to other special matrix types
-convert(::Type{Diagonal}, A::SymTridiagonal) =
+Diagonal(A::SymTridiagonal) =
     iszero(A.ev) ? Diagonal(A.dv) :
         throw(ArgumentError("matrix cannot be represented as Diagonal"))
-convert(::Type{Bidiagonal}, A::SymTridiagonal) =
+Bidiagonal(A::SymTridiagonal) =
     iszero(A.ev) ? Bidiagonal(A.dv, A.ev, :U) :
         throw(ArgumentError("matrix cannot be represented as Bidiagonal"))
-convert(::Type{Tridiagonal}, A::SymTridiagonal) =
+Tridiagonal(A::SymTridiagonal) =
     Tridiagonal(copy(A.ev), A.dv, A.ev)
 
 # conversions from Tridiagonal to other special matrix types
-convert(::Type{Diagonal}, A::Tridiagonal) =
+Diagonal(A::Tridiagonal) =
     iszero(A.dl) && iszero(A.du) ? Diagonal(A.d) :
         throw(ArgumentError("matrix cannot be represented as Diagonal"))
-convert(::Type{Bidiagonal}, A::Tridiagonal) =
+Bidiagonal(A::Tridiagonal) =
     iszero(A.dl) ? Bidiagonal(A.d, A.du, :U) :
     iszero(A.du) ? Bidiagonal(A.d, A.dl, :L) :
         throw(ArgumentError("matrix cannot be represented as Bidiagonal"))
-convert(::Type{SymTridiagonal}, A::Tridiagonal) =
+SymTridiagonal(A::Tridiagonal) =
     A.dl == A.du ? SymTridiagonal(A.d, A.dl) :
         throw(ArgumentError("matrix cannot be represented as SymTridiagonal"))
 
 # conversions from AbstractTriangular to special matrix types
-convert(::Type{Diagonal}, A::AbstractTriangular) =
+Diagonal(A::AbstractTriangular) =
     isdiag(A) ? Diagonal(diag(A)) :
         throw(ArgumentError("matrix cannot be represented as Diagonal"))
-convert(::Type{Bidiagonal}, A::AbstractTriangular) =
+Bidiagonal(A::AbstractTriangular) =
     isbanded(A, 0, 1) ? Bidiagonal(diag(A, 0), diag(A,  1), :U) : # is upper bidiagonal
     isbanded(A, -1, 0) ? Bidiagonal(diag(A, 0), diag(A, -1), :L) : # is lower bidiagonal
         throw(ArgumentError("matrix cannot be represented as Bidiagonal"))
-convert(::Type{SymTridiagonal}, A::AbstractTriangular) =
-    convert(SymTridiagonal, convert(Tridiagonal, A))
-convert(::Type{Tridiagonal}, A::AbstractTriangular) =
+SymTridiagonal(A::AbstractTriangular) = SymTridiagonal(Tridiagonal(A))
+Tridiagonal(A::AbstractTriangular) =
     isbanded(A, -1, 1) ? Tridiagonal(diag(A, -1), diag(A, 0), diag(A, 1)) : # is tridiagonal
         throw(ArgumentError("matrix cannot be represented as Tridiagonal"))
 
diff --git a/base/linalg/svd.jl b/base/linalg/svd.jl
index 1ee5eba8ad55b..a6d3bc72adb95 100644
--- a/base/linalg/svd.jl
+++ b/base/linalg/svd.jl
@@ -544,7 +544,7 @@ end
 svdvals(x::Number, y::Number) = abs(x/y)
 
 # Conversion
-convert(::Type{AbstractMatrix}, F::SVD) = (F.U * Diagonal(F.S)) * F.Vt
-convert(::Type{AbstractArray}, F::SVD) = convert(AbstractMatrix, F)
-convert(::Type{Matrix}, F::SVD) = convert(Array, convert(AbstractArray, F))
-convert(::Type{Array}, F::SVD) = convert(Matrix, F)
+AbstractMatrix(F::SVD) = (F.U * Diagonal(F.S)) * F.Vt
+AbstractArray(F::SVD) = AbstractMatrix(F)
+Matrix(F::SVD) = Array(AbstractArray(F))
+Array(F::SVD) = Matrix(F)
diff --git a/base/linalg/symmetric.jl b/base/linalg/symmetric.jl
index 1a23a84298df0..c019375b7cfcf 100644
--- a/base/linalg/symmetric.jl
+++ b/base/linalg/symmetric.jl
@@ -162,23 +162,23 @@ end
 similar(A::Union{Symmetric,Hermitian}, ::Type{T}, dims::Dims{N}) where {T,N} = similar(parent(A), T, dims)
 
 # Conversion
-convert(::Type{Matrix}, A::Symmetric) = copytri!(convert(Matrix, copy(A.data)), A.uplo)
-function convert(::Type{Matrix}, A::Hermitian)
+Matrix(A::Symmetric) = copytri!(convert(Matrix, copy(A.data)), A.uplo)
+function Matrix(A::Hermitian)
     B = copytri!(convert(Matrix, copy(A.data)), A.uplo, true)
     for i = 1:size(A, 1)
         B[i,i] = real(B[i,i])
     end
     return B
 end
-convert(::Type{Array}, A::Union{Symmetric,Hermitian}) = convert(Matrix, A)
+Array(A::Union{Symmetric,Hermitian}) = convert(Matrix, A)
 
 parent(A::HermOrSym) = A.data
-convert(::Type{Symmetric{T,S}},A::Symmetric{T,S}) where {T,S<:AbstractMatrix} = A
-convert(::Type{Symmetric{T,S}},A::Symmetric) where {T,S<:AbstractMatrix} = Symmetric{T,S}(convert(S,A.data),A.uplo)
-convert(::Type{AbstractMatrix{T}}, A::Symmetric) where {T} = Symmetric(convert(AbstractMatrix{T}, A.data), Symbol(A.uplo))
-convert(::Type{Hermitian{T,S}},A::Hermitian{T,S}) where {T,S<:AbstractMatrix} = A
-convert(::Type{Hermitian{T,S}},A::Hermitian) where {T,S<:AbstractMatrix} = Hermitian{T,S}(convert(S,A.data),A.uplo)
-convert(::Type{AbstractMatrix{T}}, A::Hermitian) where {T} = Hermitian(convert(AbstractMatrix{T}, A.data), Symbol(A.uplo))
+Symmetric{T,S}(A::Symmetric{T,S}) where {T,S<:AbstractMatrix} = A
+Symmetric{T,S}(A::Symmetric) where {T,S<:AbstractMatrix} = Symmetric{T,S}(convert(S,A.data),A.uplo)
+AbstractMatrix{T}(A::Symmetric) where {T} = Symmetric(convert(AbstractMatrix{T}, A.data), Symbol(A.uplo))
+Hermitian{T,S}(A::Hermitian{T,S}) where {T,S<:AbstractMatrix} = A
+Hermitian{T,S}(A::Hermitian) where {T,S<:AbstractMatrix} = Hermitian{T,S}(convert(S,A.data),A.uplo)
+AbstractMatrix{T}(A::Hermitian) where {T} = Hermitian(convert(AbstractMatrix{T}, A.data), Symbol(A.uplo))
 
 copy(A::Symmetric{T,S}) where {T,S} = (B = copy(A.data); Symmetric{T,typeof(B)}(B,A.uplo))
 copy(A::Hermitian{T,S}) where {T,S} = (B = copy(A.data); Hermitian{T,typeof(B)}(B,A.uplo))
diff --git a/base/linalg/triangular.jl b/base/linalg/triangular.jl
index f2d0c5a40e373..7b421e10397fb 100644
--- a/base/linalg/triangular.jl
+++ b/base/linalg/triangular.jl
@@ -13,22 +13,20 @@ for t in (:LowerTriangular, :UnitLowerTriangular, :UpperTriangular,
             data::S
         end
         $t(A::$t) = A
+        $t{T}(A::$t{T}) where {T} = A
         function $t(A::AbstractMatrix)
             Base.LinAlg.checksquare(A)
             return $t{eltype(A), typeof(A)}(A)
         end
 
-        size(A::$t, d) = size(A.data, d)
-        size(A::$t) = size(A.data)
-
-        convert(::Type{$t{T}}, A::$t{T}) where {T} = A
-        function convert(::Type{$t{T}}, A::$t) where T
+        function $t{T}(A::$t) where T
             Anew = convert(AbstractMatrix{T}, A.data)
             $t(Anew)
         end
-        convert(::Type{AbstractMatrix{T}}, A::$t{T}) where {T} = A
-        convert(::Type{AbstractMatrix{T}}, A::$t) where {T} = convert($t{T}, A)
-        convert(::Type{Matrix}, A::$t{T}) where {T} = convert(Matrix{T}, A)
+        Matrix(A::$t{T}) where {T} = Matrix{T}(A)
+
+        size(A::$t, d) = size(A.data, d)
+        size(A::$t) = size(A.data)
 
         # For A<:AbstractTriangular, similar(A[, neweltype]) should yield a matrix with the same
         # triangular type and underlying storage type as A. The following method covers these cases.
@@ -100,18 +98,18 @@ imag(A::LowerTriangular) = LowerTriangular(imag(A.data))
 imag(A::UnitLowerTriangular) = LowerTriangular(tril!(imag(A.data),-1))
 imag(A::UnitUpperTriangular) = UpperTriangular(triu!(imag(A.data),1))
 
-convert(::Type{Array}, A::AbstractTriangular) = convert(Matrix, A)
+Array(A::AbstractTriangular) = Matrix(A)
 parent(A::AbstractTriangular) = A.data
 
 # then handle all methods that requires specific handling of upper/lower and unit diagonal
 
-function convert(::Type{Matrix{T}}, A::LowerTriangular) where T
+function Matrix{T}(A::LowerTriangular) where T
     B = Matrix{T}(uninitialized, size(A, 1), size(A, 1))
     copyto!(B, A.data)
     tril!(B)
     B
 end
-function convert(::Type{Matrix{T}}, A::UnitLowerTriangular) where T
+function Matrix{T}(A::UnitLowerTriangular) where T
     B = Matrix{T}(uninitialized, size(A, 1), size(A, 1))
     copyto!(B, A.data)
     tril!(B)
@@ -120,13 +118,13 @@ function convert(::Type{Matrix{T}}, A::UnitLowerTriangular) where T
     end
     B
 end
-function convert(::Type{Matrix{T}}, A::UpperTriangular) where T
+function Matrix{T}(A::UpperTriangular) where T
     B = Matrix{T}(uninitialized, size(A, 1), size(A, 1))
     copyto!(B, A.data)
     triu!(B)
     B
 end
-function convert(::Type{Matrix{T}}, A::UnitUpperTriangular) where T
+function Matrix{T}(A::UnitUpperTriangular) where T
     B = Matrix{T}(uninitialized, size(A, 1), size(A, 1))
     copyto!(B, A.data)
     triu!(B)
diff --git a/base/linalg/tridiag.jl b/base/linalg/tridiag.jl
index a418a569ef9aa..f238c3918fa25 100644
--- a/base/linalg/tridiag.jl
+++ b/base/linalg/tridiag.jl
@@ -76,11 +76,11 @@ function SymTridiagonal(A::AbstractMatrix)
     end
 end
 
-convert(::Type{SymTridiagonal{T}}, S::SymTridiagonal) where {T} =
+SymTridiagonal{T}(S::SymTridiagonal) where {T} =
     SymTridiagonal(convert(AbstractVector{T}, S.dv), convert(AbstractVector{T}, S.ev))
-convert(::Type{AbstractMatrix{T}}, S::SymTridiagonal) where {T} =
+AbstractMatrix{T}(S::SymTridiagonal) where {T} =
     SymTridiagonal(convert(AbstractVector{T}, S.dv), convert(AbstractVector{T}, S.ev))
-function convert(::Type{Matrix{T}}, M::SymTridiagonal) where T
+function Matrix{T}(M::SymTridiagonal) where T
     n = size(M, 1)
     Mf = zeros(T, n, n)
     @inbounds begin
@@ -93,8 +93,8 @@ function convert(::Type{Matrix{T}}, M::SymTridiagonal) where T
     end
     return Mf
 end
-convert(::Type{Matrix}, M::SymTridiagonal{T}) where {T} = convert(Matrix{T}, M)
-convert(::Type{Array}, M::SymTridiagonal) = convert(Matrix, M)
+Matrix(M::SymTridiagonal{T}) where {T} = Matrix{T}(M)
+Array(M::SymTridiagonal) = Matrix(M)
 
 size(A::SymTridiagonal) = (length(A.dv), length(A.dv))
 function size(A::SymTridiagonal, d::Integer)
@@ -476,7 +476,7 @@ function size(M::Tridiagonal, d::Integer)
     end
 end
 
-function convert(::Type{Matrix{T}}, M::Tridiagonal{T}) where T
+function Matrix{T}(M::Tridiagonal{T}) where T
     A = zeros(T, size(M))
     for i = 1:length(M.d)
         A[i,i] = M.d[i]
@@ -487,8 +487,8 @@ function convert(::Type{Matrix{T}}, M::Tridiagonal{T}) where T
     end
     A
 end
-convert(::Type{Matrix}, M::Tridiagonal{T}) where {T} = convert(Matrix{T}, M)
-convert(::Type{Array}, M::Tridiagonal) = convert(Matrix, M)
+Matrix(M::Tridiagonal{T}) where {T} = Matrix{T}(M)
+Array(M::Tridiagonal) = Matrix(M)
 
 # For M<:Tridiagonal, similar(M[, neweltype]) should yield a Tridiagonal matrix.
 # On the other hand, similar(M, [neweltype,] shape...) should yield a sparse matrix.
@@ -634,11 +634,11 @@ end
 inv(A::Tridiagonal) = inv_usmani(A.dl, A.d, A.du)
 det(A::Tridiagonal) = det_usmani(A.dl, A.d, A.du)
 
-convert(::Type{Tridiagonal{T}},M::Tridiagonal) where {T} =
+Tridiagonal{T}(M::Tridiagonal) where {T} =
     Tridiagonal(convert(AbstractVector{T}, M.dl), convert(AbstractVector{T}, M.d), convert(AbstractVector{T}, M.du))
-convert(::Type{AbstractMatrix{T}},M::Tridiagonal) where {T} = convert(Tridiagonal{T}, M)
-convert(::Type{Tridiagonal{T}}, M::SymTridiagonal{T}) where {T} = Tridiagonal(M)
-function convert(::Type{SymTridiagonal{T}}, M::Tridiagonal) where T
+AbstractMatrix{T}(M::Tridiagonal) where {T} = Tridiagonal{T}(M)
+Tridiagonal{T}(M::SymTridiagonal{T}) where {T} = Tridiagonal(M)
+function SymTridiagonal{T}(M::Tridiagonal) where T
     if M.dl == M.du
         return SymTridiagonal{T}(convert(AbstractVector{T},M.d), convert(AbstractVector{T},M.dl))
     else
diff --git a/base/mpfr.jl b/base/mpfr.jl
index 016462f26937e..483903d0638fd 100644
--- a/base/mpfr.jl
+++ b/base/mpfr.jl
@@ -94,12 +94,12 @@ BigFloat(x)
 widen(::Type{Float64}) = BigFloat
 widen(::Type{BigFloat}) = BigFloat
 
-convert(::Type{BigFloat}, x::BigFloat) = x
+BigFloat(x::BigFloat) = x
 
 # convert to BigFloat
 for (fJ, fC) in ((:si,:Clong), (:ui,:Culong), (:d,:Float64))
     @eval begin
-        function convert(::Type{BigFloat}, x::($fC))
+        function BigFloat(x::($fC))
             z = BigFloat()
             ccall(($(string(:mpfr_set_,fJ)), :libmpfr), Int32, (Ref{BigFloat}, $fC, Int32), z, x, ROUNDING_MODE[])
             return z
@@ -107,19 +107,19 @@ for (fJ, fC) in ((:si,:Clong), (:ui,:Culong), (:d,:Float64))
     end
 end
 
-function convert(::Type{BigFloat}, x::BigInt)
+function BigFloat(x::BigInt)
     z = BigFloat()
     ccall((:mpfr_set_z, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigInt}, Int32), z, x, ROUNDING_MODE[])
     return z
 end
 
-convert(::Type{BigFloat}, x::Integer) = BigFloat(BigInt(x))
+BigFloat(x::Integer) = BigFloat(BigInt(x))
 
-convert(::Type{BigFloat}, x::Union{Bool,Int8,Int16,Int32}) = BigFloat(convert(Clong, x))
-convert(::Type{BigFloat}, x::Union{UInt8,UInt16,UInt32}) = BigFloat(convert(Culong, x))
+BigFloat(x::Union{Bool,Int8,Int16,Int32}) = BigFloat(convert(Clong, x))
+BigFloat(x::Union{UInt8,UInt16,UInt32}) = BigFloat(convert(Culong, x))
 
-convert(::Type{BigFloat}, x::Union{Float16,Float32}) = BigFloat(Float64(x))
-convert(::Type{BigFloat}, x::Rational) = BigFloat(numerator(x)) / BigFloat(denominator(x))
+BigFloat(x::Union{Float16,Float32}) = BigFloat(Float64(x))
+BigFloat(x::Rational) = BigFloat(numerator(x)) / BigFloat(denominator(x))
 
 function tryparse(::Type{BigFloat}, s::AbstractString, base::Int=0)
     !isempty(s) && Base.Unicode.isspace(s[end]) && return tryparse(BigFloat, rstrip(s), base)
@@ -128,8 +128,8 @@ function tryparse(::Type{BigFloat}, s::AbstractString, base::Int=0)
     err == 0 ? z : nothing
 end
 
-convert(::Type{Rational}, x::BigFloat) = convert(Rational{BigInt}, x)
-convert(::Type{AbstractFloat}, x::BigInt) = BigFloat(x)
+Rational(x::BigFloat) = convert(Rational{BigInt}, x)
+AbstractFloat(x::BigInt) = BigFloat(x)
 
 float(::Type{BigInt}) = BigFloat
 
@@ -231,32 +231,28 @@ floor(::Type{Integer}, x::BigFloat) = floor(BigInt, x)
 ceil(::Type{Integer}, x::BigFloat) = ceil(BigInt, x)
 round(::Type{Integer}, x::BigFloat) = round(BigInt, x)
 
-function convert(::Type{Bool}, x::BigFloat)
+function Bool(x::BigFloat)
     iszero(x) && return false
     isone(x) && return true
-    throw(InexactError(:convert, Bool, x))
+    throw(InexactError(:Bool, Bool, x))
 end
-function convert(::Type{BigInt},x::BigFloat)
-    isinteger(x) || throw(InexactError(:convert, BigInt, x))
-    trunc(BigInt,x)
+function BigInt(x::BigFloat)
+    isinteger(x) || throw(InexactError(:BigInt, BigInt, x))
+    trunc(BigInt, x)
 end
 
-function convert(::Type{Integer}, x::BigFloat)
-    isinteger(x) || throw(InexactError(:convert, Integer, x))
-    trunc(Integer,x)
-end
-function convert(::Type{T},x::BigFloat) where T<:Integer
-    isinteger(x) || throw(InexactError(:convert, T, x))
+function (::Type{T})(x::BigFloat) where T<:Integer
+    isinteger(x) || throw(InexactError(Symbol(string(T)), T, x))
     trunc(T,x)
 end
 
 ## BigFloat -> AbstractFloat
-convert(::Type{Float64}, x::BigFloat) =
+Float64(x::BigFloat) =
     ccall((:mpfr_get_d,:libmpfr), Float64, (Ref{BigFloat}, Int32), x, ROUNDING_MODE[])
-convert(::Type{Float32}, x::BigFloat) =
+Float32(x::BigFloat) =
     ccall((:mpfr_get_flt,:libmpfr), Float32, (Ref{BigFloat}, Int32), x, ROUNDING_MODE[])
 # TODO: avoid double rounding
-convert(::Type{Float16}, x::BigFloat) = convert(Float16, convert(Float32, x))
+Float16(x::BigFloat) = convert(Float16, convert(Float32, x))
 
 Float64(x::BigFloat, r::RoundingMode) =
     ccall((:mpfr_get_d,:libmpfr), Float64, (Ref{BigFloat}, Int32), x, to_mpfr(r))
@@ -271,7 +267,7 @@ promote_rule(::Type{BigFloat}, ::Type{<:AbstractFloat}) = BigFloat
 
 big(::Type{<:AbstractFloat}) = BigFloat
 
-function convert(::Type{Rational{BigInt}}, x::AbstractFloat)
+function (::Type{Rational{BigInt}})(x::AbstractFloat)
     isnan(x) && return zero(BigInt) // zero(BigInt)
     isinf(x) && return copysign(one(BigInt),x) // zero(BigInt)
     iszero(x) && return zero(BigInt) // one(BigInt)
diff --git a/base/number.jl b/base/number.jl
index 18f63c386f578..71090b80257c0 100644
--- a/base/number.jl
+++ b/base/number.jl
@@ -1,6 +1,11 @@
 # This file is a part of Julia. License is MIT: https://julialang.org/license
 
 ## generic operations on numbers ##
+
+# Numbers are convertible
+convert(::Type{T}, x::T)      where {T<:Number} = x
+convert(::Type{T}, x::Number) where {T<:Number} = T(x)
+
 """
     isinteger(x) -> Bool
 
diff --git a/base/pkg/read.jl b/base/pkg/read.jl
index eda9e6127390c..721ac55b907df 100644
--- a/base/pkg/read.jl
+++ b/base/pkg/read.jl
@@ -21,7 +21,7 @@ function available(names=readdir("METADATA"))
             ismatch(Base.VERSION_REGEX, ver) || continue
             isfile(versdir, ver, "sha1") || continue
             haskey(pkgs,pkg) || (pkgs[pkg] = Dict{VersionNumber,Available}())
-            pkgs[pkg][convert(VersionNumber,ver)] = Available(
+            pkgs[pkg][VersionNumber(ver)] = Available(
                 readchomp(joinpath(versdir,ver,"sha1")),
                 Reqs.parse(joinpath(versdir,ver,"requires"))
             )
@@ -41,7 +41,7 @@ function latest(names=readdir("METADATA"))
         for ver in readdir(versdir)
             ismatch(Base.VERSION_REGEX, ver) || continue
             isfile(versdir, ver, "sha1") || continue
-            push!(pkgversions, convert(VersionNumber,ver))
+            push!(pkgversions, VersionNumber(ver))
         end
         isempty(pkgversions) && continue
         ver = string(maximum(pkgversions))
diff --git a/base/pkg/reqs.jl b/base/pkg/reqs.jl
index b84ce5614993d..bcd77d733c0e8 100644
--- a/base/pkg/reqs.jl
+++ b/base/pkg/reqs.jl
@@ -28,7 +28,7 @@ struct Requirement <: Line
         package = shift!(fields)
         all(field->ismatch(Base.VERSION_REGEX, field), fields) ||
             throw(PkgError("invalid requires entry for $package: $content"))
-        versions = VersionNumber[fields...]
+        versions = map(VersionNumber, fields)
         issorted(versions) || throw(PkgError("invalid requires entry for $package: $content"))
         new(content, package, VersionSet(versions), system)
     end
diff --git a/base/pointer.jl b/base/pointer.jl
index fb4c12b57f357..95c305661652a 100644
--- a/base/pointer.jl
+++ b/base/pointer.jl
@@ -20,12 +20,10 @@ const C_NULL = bitcast(Ptr{Cvoid}, 0)
 # TODO: deprecate these conversions. C doesn't even allow them.
 
 # pointer to integer
-convert(::Type{T}, x::Ptr) where {T<:Union{Int,UInt}} = bitcast(T, x)
-convert(::Type{T}, x::Ptr) where {T<:Integer} = convert(T, convert(UInt, x))
+convert(::Type{T}, x::Ptr) where {T<:Integer} = T(UInt(x))
 
 # integer to pointer
-convert(::Type{Ptr{T}}, x::UInt) where {T} = bitcast(Ptr{T}, x)
-convert(::Type{Ptr{T}}, x::Int) where {T} = bitcast(Ptr{T}, x)
+convert(::Type{Ptr{T}}, x::Union{Int,UInt}) where {T} = Ptr{T}(x)
 
 # pointer to pointer
 convert(::Type{Ptr{T}}, p::Ptr{T}) where {T} = p
diff --git a/base/precompile.jl b/base/precompile.jl
index 72c9b57f8d220..7bde4bc345019 100644
--- a/base/precompile.jl
+++ b/base/precompile.jl
@@ -561,10 +561,6 @@ precompile(Tuple{typeof(Base.nextind), String, UInt64})
 precompile(Tuple{typeof(Base.matchall), Base.Regex, String, Bool})
 precompile(Tuple{typeof(Base.skip_deleted), Base.Dict{String, String}, Int64})
 precompile(Tuple{typeof(Base.reverse), String})
-precompile(Tuple{typeof(Core.Inference.isbits), Tuple{Nothing, Bool}})
-precompile(Tuple{typeof(Base._convert), Type{Array{Method, 1}}, Base.BitArray{1}})
-precompile(Tuple{typeof(Base.unsafe_copyto!), Array{Method, 1}, Int64, Array{Method, 1}, Int64, Int64})
-precompile(Tuple{typeof(Base.copyto!), Array{Method, 1}, Int64, Array{Method, 1}, Int64, Int64})
 precompile(Tuple{typeof(Core.Inference.length), Tuple{Core.Inference.PartialTypeVar}})
 precompile(Tuple{typeof(Core.Inference.getindex), Tuple{Core.Inference.PartialTypeVar}, Int64})
 precompile(Tuple{typeof(Base.show_delim_array), Base.GenericIOBuffer{Array{UInt8, 1}}, Array{Any, 1}, Char, Char, Char, Bool, Int64, Int64})
diff --git a/base/random/misc.jl b/base/random/misc.jl
index ff01c16e169e7..6c20d1a943d35 100644
--- a/base/random/misc.jl
+++ b/base/random/misc.jl
@@ -425,10 +425,11 @@ julia> Base.Random.uuid_version(Base.Random.uuid4(rng))
 """
 uuid_version(u::UUID) = Int((u.value >> 76) & 0xf)
 
-Base.convert(::Type{UInt128}, u::UUID) = u.value
+UInt128(u::UUID) = u.value
 
 let groupings = [1:8; 10:13; 15:18; 20:23; 25:36]
-    function Base.convert(::Type{UUID}, s::AbstractString)
+    global UUID
+    function UUID(s::AbstractString)
         s = Base.Unicode.lowercase(s)
 
         if !ismatch(r"^[0-9a-f]{8}(?:-[0-9a-f]{4}){3}-[0-9a-f]{12}$", s)
diff --git a/base/range.jl b/base/range.jl
index 3615a99a2d257..39698d436ba15 100644
--- a/base/range.jl
+++ b/base/range.jl
@@ -811,64 +811,61 @@ el_same(::Type, a, b) = typejoin(a, b)
 
 promote_rule(a::Type{UnitRange{T1}}, b::Type{UnitRange{T2}}) where {T1,T2} =
     el_same(promote_type(T1,T2), a, b)
-convert(::Type{UnitRange{T}}, r::UnitRange{T}) where {T<:Real} = r
-convert(::Type{UnitRange{T}}, r::UnitRange) where {T<:Real} = UnitRange{T}(r.start, r.stop)
+UnitRange{T}(r::UnitRange{T}) where {T<:Real} = r
+UnitRange{T}(r::UnitRange) where {T<:Real} = UnitRange{T}(r.start, r.stop)
 
 promote_rule(a::Type{OneTo{T1}}, b::Type{OneTo{T2}}) where {T1,T2} =
     el_same(promote_type(T1,T2), a, b)
-convert(::Type{OneTo{T}}, r::OneTo{T}) where {T<:Real} = r
-convert(::Type{OneTo{T}}, r::OneTo) where {T<:Real} = OneTo{T}(r.stop)
+OneTo{T}(r::OneTo{T}) where {T<:Integer} = r
+OneTo{T}(r::OneTo) where {T<:Integer} = OneTo{T}(r.stop)
 
 promote_rule(a::Type{UnitRange{T1}}, ::Type{UR}) where {T1,UR<:AbstractUnitRange} =
     promote_rule(a, UnitRange{eltype(UR)})
-convert(::Type{UnitRange{T}}, r::AbstractUnitRange) where {T<:Real} = UnitRange{T}(first(r), last(r))
-convert(::Type{UnitRange}, r::AbstractUnitRange) = UnitRange(first(r), last(r))
+UnitRange{T}(r::AbstractUnitRange) where {T<:Real} = UnitRange{T}(first(r), last(r))
+UnitRange(r::AbstractUnitRange) = UnitRange(first(r), last(r))
 
-convert(::Type{AbstractUnitRange{T}}, r::AbstractUnitRange{T}) where {T} = r
-convert(::Type{AbstractUnitRange{T}}, r::UnitRange) where {T} = convert(UnitRange{T}, r)
-convert(::Type{AbstractUnitRange{T}}, r::OneTo) where {T} = convert(OneTo{T}, r)
+AbstractUnitRange{T}(r::AbstractUnitRange{T}) where {T} = r
+AbstractUnitRange{T}(r::UnitRange) where {T} = UnitRange{T}(r)
+AbstractUnitRange{T}(r::OneTo) where {T} = OneTo{T}(r)
 
 promote_rule(::Type{StepRange{T1a,T1b}}, ::Type{StepRange{T2a,T2b}}) where {T1a,T1b,T2a,T2b} =
     el_same(promote_type(T1a,T2a),
             # el_same only operates on array element type, so just promote second type parameter
             StepRange{T1a, promote_type(T1b,T2b)},
             StepRange{T2a, promote_type(T1b,T2b)})
-convert(::Type{StepRange{T1,T2}}, r::StepRange{T1,T2}) where {T1,T2} = r
+StepRange{T1,T2}(r::StepRange{T1,T2}) where {T1,T2} = r
 
 promote_rule(a::Type{StepRange{T1a,T1b}}, ::Type{UR}) where {T1a,T1b,UR<:AbstractUnitRange} =
     promote_rule(a, StepRange{eltype(UR), eltype(UR)})
-convert(::Type{StepRange{T1,T2}}, r::AbstractRange) where {T1,T2} =
+StepRange{T1,T2}(r::AbstractRange) where {T1,T2} =
     StepRange{T1,T2}(convert(T1, first(r)), convert(T2, step(r)), convert(T1, last(r)))
-convert(::Type{StepRange}, r::AbstractUnitRange{T}) where {T} =
+StepRange(r::AbstractUnitRange{T}) where {T} =
     StepRange{T,T}(first(r), step(r), last(r))
-convert(::Type{StepRange{T1,T2} where T1}, r::AbstractRange) where {T2} =
-    convert(StepRange{eltype(r),T2}, r)
+(::Type{StepRange{T1,T2} where T1})(r::AbstractRange) where {T2} = StepRange{eltype(r),T2}(r)
 
 promote_rule(::Type{StepRangeLen{T1,R1,S1}},::Type{StepRangeLen{T2,R2,S2}}) where {T1,T2,R1,R2,S1,S2} =
     el_same(promote_type(T1,T2),
             StepRangeLen{T1,promote_type(R1,R2),promote_type(S1,S2)},
             StepRangeLen{T2,promote_type(R1,R2),promote_type(S1,S2)})
-convert(::Type{StepRangeLen{T,R,S}}, r::StepRangeLen{T,R,S}) where {T,R,S} = r
-convert(::Type{StepRangeLen{T,R,S}}, r::StepRangeLen) where {T,R,S} =
+StepRangeLen{T,R,S}(r::StepRangeLen{T,R,S}) where {T,R,S} = r
+StepRangeLen{T,R,S}(r::StepRangeLen) where {T,R,S} =
     StepRangeLen{T,R,S}(convert(R, r.ref), convert(S, r.step), length(r), r.offset)
-convert(::Type{StepRangeLen{T}}, r::StepRangeLen) where {T} =
+StepRangeLen{T}(r::StepRangeLen) where {T} =
     StepRangeLen(convert(T, r.ref), convert(T, r.step), length(r), r.offset)
 
 promote_rule(a::Type{StepRangeLen{T,R,S}}, ::Type{OR}) where {T,R,S,OR<:AbstractRange} =
     promote_rule(a, StepRangeLen{eltype(OR), eltype(OR), eltype(OR)})
-convert(::Type{StepRangeLen{T,R,S}}, r::AbstractRange) where {T,R,S} =
+StepRangeLen{T,R,S}(r::AbstractRange) where {T,R,S} =
     StepRangeLen{T,R,S}(R(first(r)), S(step(r)), length(r))
-convert(::Type{StepRangeLen{T}}, r::AbstractRange) where {T} =
+StepRangeLen{T}(r::AbstractRange) where {T} =
     StepRangeLen(T(first(r)), T(step(r)), length(r))
-convert(::Type{StepRangeLen}, r::AbstractRange) = convert(StepRangeLen{eltype(r)}, r)
+StepRangeLen(r::AbstractRange) = StepRangeLen{eltype(r)}(r)
 
 promote_rule(a::Type{LinSpace{T1}}, b::Type{LinSpace{T2}}) where {T1,T2} =
     el_same(promote_type(T1,T2), a, b)
-convert(::Type{LinSpace{T}}, r::LinSpace{T}) where {T} = r
-convert(::Type{LinSpace{T}}, r::AbstractRange) where {T} =
-    LinSpace{T}(first(r), last(r), length(r))
-convert(::Type{LinSpace}, r::AbstractRange{T}) where {T} =
-    convert(LinSpace{T}, r)
+LinSpace{T}(r::LinSpace{T}) where {T} = r
+LinSpace{T}(r::AbstractRange) where {T} = LinSpace{T}(first(r), last(r), length(r))
+LinSpace(r::AbstractRange{T}) where {T} = LinSpace{T}(r)
 
 promote_rule(a::Type{LinSpace{T}}, ::Type{OR}) where {T,OR<:OrdinalRange} =
     promote_rule(a, LinSpace{eltype(OR)})
@@ -894,7 +891,7 @@ function vcat(rs::AbstractRange{T}...) where T
     return a
 end
 
-convert(::Type{Array{T,1}}, r::AbstractRange{T}) where {T} = vcat(r)
+Array{T,1}(r::AbstractRange{T}) where {T} = vcat(r)
 collect(r::AbstractRange) = vcat(r)
 
 reverse(r::OrdinalRange) = colon(last(r), -step(r), first(r))
diff --git a/base/rational.jl b/base/rational.jl
index 43a4332b512fb..cf0c3de1e5749 100644
--- a/base/rational.jl
+++ b/base/rational.jl
@@ -74,32 +74,29 @@ function write(s::IO, z::Rational)
     write(s,numerator(z),denominator(z))
 end
 
-convert(::Type{Rational{T}}, x::Rational) where {T<:Integer} = Rational{T}(convert(T,x.num),convert(T,x.den))
-convert(::Type{Rational{T}}, x::Integer) where {T<:Integer} = Rational{T}(convert(T,x), convert(T,1))
+Rational{T}(x::Rational) where {T<:Integer} = Rational{T}(convert(T,x.num), convert(T,x.den))
+Rational{T}(x::Integer) where {T<:Integer} = Rational{T}(convert(T,x), convert(T,1))
 
-convert(::Type{Rational}, x::Rational) = x
-convert(::Type{Rational}, x::Integer) = convert(Rational{typeof(x)},x)
+Rational(x::Rational) = x
 
-convert(::Type{Bool}, x::Rational) = x==0 ? false : x==1 ? true :
-    throw(InexactError(:convert, Bool, x)) # to resolve ambiguity
-convert(::Type{Integer}, x::Rational) = (isinteger(x) ? convert(Integer, x.num) :
-    throw(InexactError(:convert, Integer, x)))
-convert(::Type{T}, x::Rational) where {T<:Integer} = (isinteger(x) ? convert(T, x.num) :
-    throw(InexactError(:convert, T, x)))
+Bool(x::Rational) = x==0 ? false : x==1 ? true :
+    throw(InexactError(:Bool, Bool, x)) # to resolve ambiguity
+(::Type{T})(x::Rational) where {T<:Integer} = (isinteger(x) ? convert(T, x.num) :
+    throw(InexactError(Symbol(string(T)), T, x)))
 
-convert(::Type{AbstractFloat}, x::Rational) = float(x.num)/float(x.den)
-function convert(::Type{T}, x::Rational{S}) where T<:AbstractFloat where S
+AbstractFloat(x::Rational) = float(x.num)/float(x.den)
+function (::Type{T})(x::Rational{S}) where T<:AbstractFloat where S
     P = promote_type(T,S)
     convert(T, convert(P,x.num)/convert(P,x.den))
 end
 
-function convert(::Type{Rational{T}}, x::AbstractFloat) where T<:Integer
+function Rational{T}(x::AbstractFloat) where T<:Integer
     r = rationalize(T, x, tol=0)
-    x == convert(typeof(x), r) || throw(InexactError(:convert, Rational{T}, x))
+    x == convert(typeof(x), r) || throw(InexactError(:Rational, Rational{T}, x))
     r
 end
-convert(::Type{Rational}, x::Float64) = convert(Rational{Int64}, x)
-convert(::Type{Rational}, x::Float32) = convert(Rational{Int}, x)
+Rational(x::Float64) = Rational{Int64}(x)
+Rational(x::Float32) = Rational{Int}(x)
 
 big(z::Complex{<:Rational{<:Integer}}) = Complex{Rational{BigInt}}(z)
 
diff --git a/base/replutil.jl b/base/replutil.jl
index 6d93f4dce3761..8ad88cef24d0e 100644
--- a/base/replutil.jl
+++ b/base/replutil.jl
@@ -412,16 +412,6 @@ function showerror(io::IO, ex::MethodError)
                       "\nYou can convert to a column vector with the vec() function.")
         end
     end
-    # Give a helpful error message if the user likely called a type constructor
-    # and sees a no method error for convert
-    if (f === Base.convert && !isempty(arg_types_param) && !is_arg_types &&
-        isa(arg_types_param[1], DataType) &&
-        arg_types_param[1].name === Type.body.name)
-        construct_type = arg_types_param[1].parameters[1]
-        println(io)
-        print(io, "This may have arisen from a call to the constructor $construct_type(...),",
-                  "\nsince type constructors fall back to convert methods.")
-    end
     try
         show_method_candidates(io, ex, kwargs)
     catch ex
@@ -712,7 +702,7 @@ Determines whether a method is the default method which is provided to all types
 Such a method is usually undesirable to be displayed to the user in the REPL.
 """
 function is_default_method(m::Method)
-    return m.module == Base && m.file == Symbol("sysimg.jl") && m.sig == Tuple{Type{T},Any} where T
+    return m.module == Base && m.sig == Tuple{Type{T},Any} where T
 end
 
 @noinline function throw_eachindex_mismatch(::IndexLinear, A...)
diff --git a/base/set.jl b/base/set.jl
index b708916058f43..8c1b03c893d7e 100644
--- a/base/set.jl
+++ b/base/set.jl
@@ -22,7 +22,7 @@ for sets of arbitrary objects.
 """
 Set(itr) = Set{eltype(itr)}(itr)
 function Set(g::Generator)
-    T = @default_eltype(typeof(g))
+    T = @default_eltype(g)
     (_isleaftype(T) || T === Union{}) || return grow_to!(Set{T}(), g)
     return Set{T}(g)
 end
@@ -329,7 +329,7 @@ julia> unique(Real[1, 1.0, 2])
 ```
 """
 function unique(itr)
-    T = @default_eltype(typeof(itr))
+    T = @default_eltype(itr)
     out = Vector{T}()
     seen = Set{T}()
     i = start(itr)
@@ -542,5 +542,5 @@ function hash(s::Set, h::UInt)
     hash(hv, h)
 end
 
-convert(::Type{Set{T}}, s::Set{T}) where {T} = s
-convert(::Type{Set{T}}, x::Set) where {T} = Set{T}(x)
+convert(::Type{T}, s::T) where {T<:AbstractSet} = s
+convert(::Type{T}, s::AbstractSet) where {T<:AbstractSet} = T(s)
diff --git a/base/socket.jl b/base/socket.jl
index 57dc7dd0278cf..5e061f305aeb5 100644
--- a/base/socket.jl
+++ b/base/socket.jl
@@ -4,7 +4,7 @@
 abstract type IPAddr end
 
 Base.isless(a::T, b::T) where {T<:IPAddr} = isless(a.host, b.host)
-Base.convert(dt::Type{<:Integer}, ip::IPAddr) = dt(ip.host)
+(dt::Type{<:Integer})(ip::IPAddr) = dt(ip.host)::dt
 
 struct IPv4 <: IPAddr
     host::UInt32
diff --git a/base/sparse/sparse.jl b/base/sparse/sparse.jl
index 3199fea8e3f0e..3cad4648c8c06 100644
--- a/base/sparse/sparse.jl
+++ b/base/sparse/sparse.jl
@@ -27,7 +27,7 @@ import Base: @get!, acos, acosd, acot, acotd, acsch, asech, asin, asind, asinh,
     vcat, hcat, hvcat, cat, imag, indmax, ishermitian, kron, length, log, log1p, max, min,
     maximum, minimum, norm, one, promote_eltype, real, reshape, rot180,
     rotl90, rotr90, round, scale!, setindex!, similar, size, transpose, tril,
-    triu, vec, permute!, map, map!
+    triu, vec, permute!, map, map!, Array
 
 export AbstractSparseArray, AbstractSparseMatrix, AbstractSparseVector,
     SparseMatrixCSC, SparseVector, blkdiag, droptol!, dropzeros!, dropzeros,
diff --git a/base/sparse/sparsematrix.jl b/base/sparse/sparsematrix.jl
index 1c62160478a4c..b864016b94f11 100644
--- a/base/sparse/sparsematrix.jl
+++ b/base/sparse/sparsematrix.jl
@@ -349,31 +349,30 @@ similar(S::SparseMatrixCSC, ::Type{TvNew}, ::Type{TiNew}, m::Integer, n::Integer
     _sparsesimilar(S, TvNew, TiNew, (m, n))
 
 
-# convert'ing between SparseMatrixCSC types
-convert(::Type{AbstractMatrix{Tv}}, A::SparseMatrixCSC{Tv}) where {Tv} = A
-convert(::Type{AbstractMatrix{Tv}}, A::SparseMatrixCSC) where {Tv} = convert(SparseMatrixCSC{Tv}, A)
-convert(::Type{SparseMatrixCSC{Tv}}, S::SparseMatrixCSC{Tv}) where {Tv} = S
-convert(::Type{SparseMatrixCSC{Tv}}, S::SparseMatrixCSC) where {Tv} = convert(SparseMatrixCSC{Tv,eltype(S.colptr)}, S)
-convert(::Type{SparseMatrixCSC{Tv,Ti}}, S::SparseMatrixCSC{Tv,Ti}) where {Tv,Ti} = S
-function convert(::Type{SparseMatrixCSC{Tv,Ti}}, S::SparseMatrixCSC) where {Tv,Ti}
+# converting between SparseMatrixCSC types
+AbstractMatrix{Tv}(A::SparseMatrixCSC) where {Tv} = SparseMatrixCSC{Tv}(A)
+SparseMatrixCSC{Tv}(S::SparseMatrixCSC{Tv}) where {Tv} = copy(S)
+SparseMatrixCSC{Tv}(S::SparseMatrixCSC) where {Tv} = SparseMatrixCSC{Tv,eltype(S.colptr)}(S)
+SparseMatrixCSC{Tv,Ti}(S::SparseMatrixCSC{Tv,Ti}) where {Tv,Ti} = copy(S)
+function SparseMatrixCSC{Tv,Ti}(S::SparseMatrixCSC) where {Tv,Ti}
     eltypeTicolptr = convert(Vector{Ti}, S.colptr)
     eltypeTirowval = convert(Vector{Ti}, S.rowval)
     eltypeTvnzval = convert(Vector{Tv}, S.nzval)
     return SparseMatrixCSC(S.m, S.n, eltypeTicolptr, eltypeTirowval, eltypeTvnzval)
 end
-# convert'ing from other matrix types to SparseMatrixCSC (also see sparse())
-convert(::Type{SparseMatrixCSC}, M::Matrix) = sparse(M)
-convert(::Type{SparseMatrixCSC}, M::AbstractMatrix{Tv}) where {Tv} = convert(SparseMatrixCSC{Tv,Int}, M)
-convert(::Type{SparseMatrixCSC{Tv}}, M::AbstractMatrix{Tv}) where {Tv} = convert(SparseMatrixCSC{Tv,Int}, M)
-function convert(::Type{SparseMatrixCSC{Tv,Ti}}, M::AbstractMatrix) where {Tv,Ti}
+# converting from other matrix types to SparseMatrixCSC (also see sparse())
+SparseMatrixCSC(M::Matrix) = sparse(M)
+SparseMatrixCSC(M::AbstractMatrix{Tv}) where {Tv} = SparseMatrixCSC{Tv,Int}(M)
+SparseMatrixCSC{Tv}(M::AbstractMatrix{Tv}) where {Tv} = SparseMatrixCSC{Tv,Int}(M)
+function SparseMatrixCSC{Tv,Ti}(M::AbstractMatrix) where {Tv,Ti}
     (I, J, V) = findnz(M)
     eltypeTiI = convert(Vector{Ti}, I)
     eltypeTiJ = convert(Vector{Ti}, J)
     eltypeTvV = convert(Vector{Tv}, V)
     return sparse_IJ_sorted!(eltypeTiI, eltypeTiJ, eltypeTvV, size(M)...)
 end
-# convert'ing from SparseMatrixCSC to other matrix types
-function convert(::Type{Matrix}, S::SparseMatrixCSC{Tv}) where Tv
+# converting from SparseMatrixCSC to other matrix types
+function Matrix(S::SparseMatrixCSC{Tv}) where Tv
     # Handle cases where zero(Tv) is not defined but the array is dense.
     A = length(S) == nnz(S) ? Matrix{Tv}(uninitialized, S.m, S.n) : zeros(Tv, S.m, S.n)
     for Sj in 1:S.n
@@ -385,7 +384,7 @@ function convert(::Type{Matrix}, S::SparseMatrixCSC{Tv}) where Tv
     end
     return A
 end
-convert(::Type{Array}, S::SparseMatrixCSC) = convert(Matrix, S)
+Array(S::SparseMatrixCSC) = Matrix(S)
 
 float(S::SparseMatrixCSC) = SparseMatrixCSC(S.m, S.n, copy(S.colptr), copy(S.rowval), float.(S.nzval))
 complex(S::SparseMatrixCSC) = SparseMatrixCSC(S.m, S.n, copy(S.colptr), copy(S.rowval), complex(copy(S.nzval)))
diff --git a/base/sparse/sparsevector.jl b/base/sparse/sparsevector.jl
index b02f62724ca11..3941849f5be90 100644
--- a/base/sparse/sparsevector.jl
+++ b/base/sparse/sparsevector.jl
@@ -342,16 +342,14 @@ end
 ### Conversion
 
 # convert SparseMatrixCSC to SparseVector
-function convert(::Type{SparseVector{Tv,Ti}}, s::SparseMatrixCSC{Tv,Ti}) where {Tv,Ti<:Integer}
+function SparseVector{Tv,Ti}(s::SparseMatrixCSC{Tv,Ti}) where {Tv,Ti<:Integer}
     size(s, 2) == 1 || throw(ArgumentError("The input argument must have a single-column."))
     SparseVector(s.m, s.rowval, s.nzval)
 end
 
-convert(::Type{SparseVector{Tv}}, s::SparseMatrixCSC{Tv,Ti}) where {Tv,Ti} =
-    convert(SparseVector{Tv,Ti}, s)
+SparseVector{Tv}(s::SparseMatrixCSC{Tv,Ti}) where {Tv,Ti} = SparseVector{Tv,Ti}(s)
 
-convert(::Type{SparseVector}, s::SparseMatrixCSC{Tv,Ti}) where {Tv,Ti} =
-    convert(SparseVector{Tv,Ti}, s)
+SparseVector(s::SparseMatrixCSC{Tv,Ti}) where {Tv,Ti} = SparseVector{Tv,Ti}(s)
 
 # convert Vector to SparseVector
 
@@ -369,7 +367,7 @@ julia> sparsevec([1.0, 2.0, 0.0, 0.0, 3.0, 0.0])
   [5]  =  3.0
 ```
 """
-sparsevec(a::AbstractVector{T}) where {T} = convert(SparseVector{T, Int}, a)
+sparsevec(a::AbstractVector{T}) where {T} = SparseVector{T, Int}(a)
 sparsevec(a::AbstractArray) = sparsevec(vec(a))
 sparsevec(a::AbstractSparseArray) = vec(a)
 sparsevec(a::AbstractSparseVector) = vec(a)
@@ -402,23 +400,21 @@ function _dense2sparsevec(s::AbstractArray{Tv}, initcap::Ti) where {Tv,Ti}
     SparseVector(n, nzind, nzval)
 end
 
-convert(::Type{SparseVector{Tv,Ti}}, s::AbstractVector{Tv}) where {Tv,Ti} =
+SparseVector{Tv,Ti}(s::AbstractVector{Tv}) where {Tv,Ti} =
     _dense2sparsevec(s, convert(Ti, max(8, div(length(s), 8))))
 
-convert(::Type{SparseVector{Tv}}, s::AbstractVector{Tv}) where {Tv} =
-    convert(SparseVector{Tv,Int}, s)
+SparseVector{Tv}(s::AbstractVector{Tv}) where {Tv} = SparseVector{Tv,Int}(s)
 
-convert(::Type{SparseVector}, s::AbstractVector{Tv}) where {Tv} =
-    convert(SparseVector{Tv,Int}, s)
+SparseVector(s::AbstractVector{Tv}) where {Tv} = SparseVector{Tv,Int}(s)
 
 
 # convert between different types of SparseVector
-convert(::Type{SparseVector{Tv}}, s::SparseVector{Tv}) where {Tv} = s
-convert(::Type{SparseVector{Tv,Ti}}, s::SparseVector{Tv,Ti}) where {Tv,Ti} = s
-convert(::Type{SparseVector{Tv,Ti}}, s::SparseVector) where {Tv,Ti} =
+SparseVector{Tv}(s::SparseVector{Tv}) where {Tv} = s
+SparseVector{Tv,Ti}(s::SparseVector{Tv,Ti}) where {Tv,Ti} = s
+SparseVector{Tv,Ti}(s::SparseVector) where {Tv,Ti} =
     SparseVector{Tv,Ti}(s.n, convert(Vector{Ti}, s.nzind), convert(Vector{Tv}, s.nzval))
 
-convert(::Type{SparseVector{Tv}}, s::SparseVector{<:Any,Ti}) where {Tv,Ti} =
+SparseVector{Tv}(s::SparseVector{<:Any,Ti}) where {Tv,Ti} =
     SparseVector{Tv,Ti}(s.n, s.nzind, convert(Vector{Tv}, s.nzval))
 
 
@@ -843,7 +839,7 @@ end
 
 ### Conversion to matrix
 
-function convert(::Type{SparseMatrixCSC{Tv,Ti}}, x::AbstractSparseVector) where {Tv,Ti}
+function SparseMatrixCSC{Tv,Ti}(x::AbstractSparseVector) where {Tv,Ti}
     n = length(x)
     xnzind = nonzeroinds(x)
     xnzval = nonzeros(x)
@@ -856,13 +852,11 @@ function convert(::Type{SparseMatrixCSC{Tv,Ti}}, x::AbstractSparseVector) where
     SparseMatrixCSC(n, 1, colptr, rowval, nzval)
 end
 
-convert(::Type{SparseMatrixCSC{Tv}}, x::AbstractSparseVector{<:Any,Ti}) where {Tv,Ti} =
-    convert(SparseMatrixCSC{Tv,Ti}, x)
+SparseMatrixCSC{Tv}(x::AbstractSparseVector{<:Any,Ti}) where {Tv,Ti} = SparseMatrixCSC{Tv,Ti}(x)
 
-convert(::Type{SparseMatrixCSC}, x::AbstractSparseVector{Tv,Ti}) where {Tv,Ti} =
-    convert(SparseMatrixCSC{Tv,Ti}, x)
+SparseMatrixCSC(x::AbstractSparseVector{Tv,Ti}) where {Tv,Ti} = SparseMatrixCSC{Tv,Ti}(x)
 
-function convert(::Type{Vector}, x::AbstractSparseVector{Tv}) where Tv
+function Vector(x::AbstractSparseVector{Tv}) where Tv
     n = length(x)
     n == 0 && return Vector{Tv}()
     nzind = nonzeroinds(x)
@@ -875,7 +869,7 @@ function convert(::Type{Vector}, x::AbstractSparseVector{Tv}) where Tv
     end
     return r
 end
-convert(::Type{Array}, x::AbstractSparseVector) = convert(Vector, x)
+Array(x::AbstractSparseVector) = Vector(x)
 
 ### Array manipulation
 
diff --git a/base/statistics.jl b/base/statistics.jl
index a866a5ed28315..aead894107d8b 100644
--- a/base/statistics.jl
+++ b/base/statistics.jl
@@ -708,14 +708,14 @@ end
     T  = promote_type(eltype(v), typeof(v[1]*h))
 
     if h == 0
-        return T(v[i])
+        return convert(T, v[i])
     else
         a = v[i]
         b = v[i+1]
         if isfinite(a) && isfinite(b)
-            return T(a + h*(b-a))
+            return convert(T, a + h*(b-a))
         else
-            return T((1-h)*a + h*b)
+            return convert(T, (1-h)*a + h*b)
         end
     end
 end
diff --git a/base/strings/basic.jl b/base/strings/basic.jl
index 0f8d8f462d703..703e455a6306b 100644
--- a/base/strings/basic.jl
+++ b/base/strings/basic.jl
@@ -605,7 +605,7 @@ julia> repeat("ha", 3)
 "hahaha"
 ```
 """
-repeat(s::AbstractString, r::Integer) = repeat(convert(String, s), r)
+repeat(s::AbstractString, r::Integer) = repeat(String(s), r)
 
 """
     ^(s::Union{AbstractString,Char}, n::Integer)
diff --git a/base/strings/io.jl b/base/strings/io.jl
index 06912b6c37578..538d7a55242e6 100644
--- a/base/strings/io.jl
+++ b/base/strings/io.jl
@@ -496,7 +496,7 @@ function unindent(str::AbstractString, indent::Int; tabwidth=8)
     String(take!(buf))
 end
 
-function convert(::Type{String}, chars::AbstractVector{Char})
+function String(chars::AbstractVector{Char})
     sprint(sizehint=length(chars)) do io
         for c in chars
             write(io, c)
diff --git a/base/strings/string.jl b/base/strings/string.jl
index b3b442e030932..888cda75c6046 100644
--- a/base/strings/string.jl
+++ b/base/strings/string.jl
@@ -58,7 +58,7 @@ Convert a string to a contiguous byte array representation encoded as UTF-8 byte
 This representation is often appropriate for passing strings to C.
 """
 String(s::AbstractString) = print_to_string(s)
-String(s::Symbol) = unsafe_string(Cstring(s))
+String(s::Symbol) = unsafe_string(unsafe_convert(Ptr{UInt8}, s))
 
 (::Type{Vector{UInt8}})(s::String) = ccall(:jl_string_to_array, Ref{Vector{UInt8}}, (Any,), s)
 
diff --git a/base/strings/util.jl b/base/strings/util.jl
index c709f94ff46b3..152762db334cf 100644
--- a/base/strings/util.jl
+++ b/base/strings/util.jl
@@ -561,4 +561,4 @@ julia> ascii("abcdefgh")
 "abcdefgh"
 ```
 """
-ascii(x::AbstractString) = ascii(convert(String, x))
+ascii(x::AbstractString) = ascii(String(x))
diff --git a/base/sysimg.jl b/base/sysimg.jl
index b10f6f1ebc1b3..616b2e10f27db 100644
--- a/base/sysimg.jl
+++ b/base/sysimg.jl
@@ -119,10 +119,6 @@ include("refpointer.jl")
 include("checked.jl")
 using .Checked
 
-# buggy handling of ispure in type-inference means this should be
-# after re-defining the basic operations that they might try to call
-(::Type{T})(arg) where {T} = convert(T, arg)::T # Hidden from the REPL.
-
 # vararg Symbol constructor
 Symbol(x...) = Symbol(string(x...))
 
diff --git a/base/twiceprecision.jl b/base/twiceprecision.jl
index 06108e505c35a..bc47ea3f2bb6d 100644
--- a/base/twiceprecision.jl
+++ b/base/twiceprecision.jl
@@ -240,12 +240,15 @@ promote_rule(::Type{TwicePrecision{R}}, ::Type{TwicePrecision{S}}) where {R,S} =
 promote_rule(::Type{TwicePrecision{R}}, ::Type{S}) where {R,S} =
     TwicePrecision{promote_type(R,S)}
 
+(::Type{T})(x::TwicePrecision) where {T<:Number} = T(x.hi + x.lo)::T
+TwicePrecision{T}(x::Number) where {T} = TwicePrecision{T}(T(x), zero(T))
+
 convert(::Type{TwicePrecision{T}}, x::TwicePrecision{T}) where {T} = x
 convert(::Type{TwicePrecision{T}}, x::TwicePrecision) where {T} =
     TwicePrecision{T}(convert(T, x.hi), convert(T, x.lo))
 
-convert(::Type{T}, x::TwicePrecision) where {T<:Number} = convert(T, x.hi + x.lo)
-convert(::Type{TwicePrecision{T}}, x::Number) where {T} = TwicePrecision{T}(convert(T, x), zero(T))
+convert(::Type{T}, x::TwicePrecision) where {T<:Number} = T(x)
+convert(::Type{TwicePrecision{T}}, x::Number) where {T} = TwicePrecision{T}(x)
 
 float(x::TwicePrecision{<:AbstractFloat}) = x
 float(x::TwicePrecision) = TwicePrecision(float(x.hi), float(x.lo))
@@ -476,19 +479,19 @@ end
 /(r::StepRangeLen{<:Real,<:TwicePrecision}, x::Real) =
     StepRangeLen(r.ref/x, twiceprecision(r.step/x, nbitslen(r)), length(r), r.offset)
 
-convert(::Type{StepRangeLen{T,R,S}}, r::StepRangeLen{T,R,S}) where {T<:AbstractFloat,R<:TwicePrecision,S<:TwicePrecision} = r
+StepRangeLen{T,R,S}(r::StepRangeLen{T,R,S}) where {T<:AbstractFloat,R<:TwicePrecision,S<:TwicePrecision} = r
 
-convert(::Type{StepRangeLen{T,R,S}}, r::StepRangeLen) where {T<:AbstractFloat,R<:TwicePrecision,S<:TwicePrecision} =
+StepRangeLen{T,R,S}(r::StepRangeLen) where {T<:AbstractFloat,R<:TwicePrecision,S<:TwicePrecision} =
     _convertSRL(StepRangeLen{T,R,S}, r)
 
-convert(::Type{StepRangeLen{Float64}}, r::StepRangeLen) =
+(::Type{StepRangeLen{Float64}})(r::StepRangeLen) =
     _convertSRL(StepRangeLen{Float64,TwicePrecision{Float64},TwicePrecision{Float64}}, r)
-convert(::Type{StepRangeLen{T}}, r::StepRangeLen) where {T<:IEEEFloat} =
+StepRangeLen{T}(r::StepRangeLen) where {T<:IEEEFloat} =
     _convertSRL(StepRangeLen{T,Float64,Float64}, r)
 
-convert(::Type{StepRangeLen{Float64}}, r::AbstractRange) =
+(::Type{StepRangeLen{Float64}})(r::AbstractRange) =
     _convertSRL(StepRangeLen{Float64,TwicePrecision{Float64},TwicePrecision{Float64}}, r)
-convert(::Type{StepRangeLen{T}}, r::AbstractRange) where {T<:IEEEFloat} =
+StepRangeLen{T}(r::AbstractRange) where {T<:IEEEFloat} =
     _convertSRL(StepRangeLen{T,Float64,Float64}, r)
 
 function _convertSRL(::Type{StepRangeLen{T,R,S}}, r::StepRangeLen{<:Integer}) where {T,R,S}
diff --git a/base/version.jl b/base/version.jl
index 7ccbf138aa0a7..66cc198466d9f 100644
--- a/base/version.jl
+++ b/base/version.jl
@@ -47,6 +47,8 @@ VersionNumber(major::Integer, minor::Integer = 0, patch::Integer = 0,
         map(x->x isa Integer ? UInt64(x) : String(x), pre),
         map(x->x isa Integer ? UInt64(x) : String(x), bld))
 
+VersionNumber(v::Tuple) = VersionNumber(v...)
+
 function print(io::IO, v::VersionNumber)
     v == typemax(VersionNumber) && return print(io, "∞")
     print(io, v.major)
@@ -65,9 +67,6 @@ function print(io::IO, v::VersionNumber)
 end
 show(io::IO, v::VersionNumber) = print(io, "v\"", v, "\"")
 
-convert(::Type{VersionNumber}, v::Integer) = VersionNumber(v)
-convert(::Type{VersionNumber}, v::Tuple) = VersionNumber(v...)
-
 const VERSION_REGEX = r"^
     v?                                      # prefix        (optional)
     (\d+)                                   # major         (required)
@@ -104,8 +103,6 @@ function VersionNumber(v::AbstractString)
     return VersionNumber(major, minor, patch, prerl, build)
 end
 
-convert(::Type{VersionNumber}, v::AbstractString) = VersionNumber(v)
-
 macro v_str(v); VersionNumber(v); end
 
 typemin(::Type{VersionNumber}) = v"0-"
@@ -215,7 +212,7 @@ A `VersionNumber` object describing which version of Julia is in use. For detail
 [Version Number Literals](@ref man-version-number-literals).
 """
 const VERSION = try
-    ver = convert(VersionNumber, VERSION_STRING)
+    ver = VersionNumber(VERSION_STRING)
     if !isempty(ver.prerelease)
         if GIT_VERSION_INFO.build_number >= 0
             ver = VersionNumber(ver.major, ver.minor, ver.patch, (ver.prerelease..., GIT_VERSION_INFO.build_number), ver.build)
@@ -232,7 +229,7 @@ catch e
     VersionNumber(0)
 end
 
-const libllvm_version = convert(VersionNumber, libllvm_version_string)
+const libllvm_version = VersionNumber(libllvm_version_string)
 
 function banner(io::IO = STDOUT)
     if GIT_VERSION_INFO.tagged_commit
diff --git a/base/weakkeydict.jl b/base/weakkeydict.jl
index ecda0680dda10..fb153d500d96e 100644
--- a/base/weakkeydict.jl
+++ b/base/weakkeydict.jl
@@ -70,21 +70,6 @@ end
 
 empty(d::WeakKeyDict, ::Type{K}, ::Type{V}) where {K, V} = WeakKeyDict{K, V}()
 
-# conversion between Dict types
-function convert(::Type{WeakKeyDict{K,V}},d::AbstractDict) where V where K
-    h = WeakKeyDict{K,V}()
-    for (k,v) in d
-        ck = convert(K,k)
-        if !haskey(h,ck)
-            h[ck] = convert(V,v)
-        else
-            error("key collision during dictionary conversion")
-        end
-    end
-    return h
-end
-convert(::Type{WeakKeyDict{K,V}},d::WeakKeyDict{K,V}) where {K,V} = d
-
 islocked(wkh::WeakKeyDict) = islocked(wkh.lock)
 lock(f, wkh::WeakKeyDict) = lock(f, wkh.lock)
 trylock(f, wkh::WeakKeyDict) = trylock(f, wkh.lock)
diff --git a/doc/src/manual/constructors.md b/doc/src/manual/constructors.md
index 330ed28bd8625..7aef476e97ae9 100644
--- a/doc/src/manual/constructors.md
+++ b/doc/src/manual/constructors.md
@@ -504,29 +504,6 @@ of its arguments are complex integers, it will return an instance of `Complex{Ou
 The interested reader should consider perusing the rest of [`rational.jl`](https://github.com/JuliaLang/julia/blob/master/base/rational.jl):
 it is short, self-contained, and implements an entire basic Julia type.
 
-## [Constructors and Conversion](@id constructors-and-conversion)
-
-Constructors `T(args...)` in Julia are implemented like other callable objects: methods are added
-to their types. The type of a type is `Type`, so all constructor methods are stored in the method
-table for the `Type` type. This means that you can declare more flexible constructors, e.g. constructors
-for abstract types, by explicitly defining methods for the appropriate types.
-
-However, in some cases you could consider adding methods to `Base.convert` *instead* of defining
-a constructor, because Julia falls back to calling [`convert`](@ref) if no matching constructor
-is found. For example, if no constructor `T(args...) = ...` exists `Base.convert(::Type{T}, args...) = ...`
-is called.
-
-`convert` is used extensively throughout Julia whenever one type needs to be converted to another
-(e.g. in assignment, [`ccall`](@ref), etcetera), and should generally only be defined (or successful)
-if the conversion is lossless.  For example, `convert(Int, 3.0)` produces `3`, but `convert(Int, 3.2)`
-throws an `InexactError`.  If you want to define a constructor for a lossless conversion from
-one type to another, you should probably define a `convert` method instead.
-
-On the other hand, if your constructor does not represent a lossless conversion, or doesn't represent
-"conversion" at all, it is better to leave it as a constructor rather than a `convert` method.
-For example, the `Array{Int,0}(uninitialized)` constructor creates a zero-dimensional `Array` of the type `Int`,
-but is not really a "conversion" from `Int` to an `Array`.
-
 ## Outer-only constructors
 
 As we have seen, a typical parametric type has inner constructors that are called when type parameters
diff --git a/doc/src/manual/conversion-and-promotion.md b/doc/src/manual/conversion-and-promotion.md
index 4c4a823db56a3..56fe28341b089 100644
--- a/doc/src/manual/conversion-and-promotion.md
+++ b/doc/src/manual/conversion-and-promotion.md
@@ -41,10 +41,17 @@ of promotion rules defining what types they should promote to when mixed with ot
 
 ## Conversion
 
-Conversion of values to various types is performed by the `convert` function. The `convert` function
-generally takes two arguments: the first is a type object while the second is a value to convert
-to that type; the returned value is the value converted to an instance of given type. The simplest
-way to understand this function is to see it in action:
+The standard way to obtain a value of a certain type `T` is to call the type's constructor, `T(x)`.
+However, there are cases where it's convenient to convert a value from one type to another
+without the programmer asking for it explicitly.
+One example is assigning a value into an array: if `A` is a `Vector{Float64}`, the expression
+`A[1] = 2` should work by automatically converting the `2` from `Int` to `Float64`, and
+storing the result in the array.
+This is done via the `convert` function.
+
+The `convert` function generally takes two arguments: the first is a type object and the second is
+a value to convert to that type. The returned value is the value converted to an instance of given type.
+The simplest way to understand this function is to see it in action:
 
 ```jldoctest
 julia> x = 12
@@ -81,9 +88,7 @@ doesn't know how to perform the requested conversion:
 
 ```jldoctest
 julia> convert(AbstractFloat, "foo")
-ERROR: MethodError: Cannot `convert` an object of type String to an object of type AbstractFloat
-This may have arisen from a call to the constructor AbstractFloat(...),
-since type constructors fall back to convert methods.
+ERROR: MethodError: Cannot `convert` an object of type String to an object of type AbstractFloat.
 ```
 
 Some languages consider parsing strings as numbers or formatting numbers as strings to be conversions
@@ -92,93 +97,77 @@ not: even though some strings can be parsed as numbers, most strings are not val
 of numbers, and only a very limited subset of them are. Therefore in Julia the dedicated `parse`
 function must be used to perform this operation, making it more explicit.
 
+### When is `convert` called?
+
+The following language constructs call `convert`:
+
+  * Assigning to an array converts to the array's element type.
+  * Assigning to a field of an object converts to the declared type of the field.
+  * Constructing an object with `new` converts to the object's declared field types.
+  * Assigning to a variable with a declared type (e.g. `local x::T`) converts to that type.
+  * A function with a declared return type converts its return value to that type.
+  * Passing a value to `ccall` converts it to the corresponding argument type.
+
+### Conversion vs. Construction
+
+Note that the behavior of `convert(T, x)` appears to be nearly identical to `T(x)`.
+Indeed, it usually is.
+However, there is a key semantic difference: since `convert` can be called implicitly,
+its methods are restricted to cases that are considered "safe" or "unsurprising".
+`convert` will only convert between types that represent the same basic kind of thing
+(e.g. different representations of numbers, or different string encodings).
+It is also usually lossless; converting a value to a different type and back again
+should result in the exact same value.
+
+Notice that some constructors don't implement the concept of "conversion".
+For example, `Vector{Int}(5)` constructs a 5-element vector, which is not really a
+"conversion" from an integer to a vector.
+
+Finally, `convert(T, x)` is expected to return the original `x` if `x` is already of type `T`.
+In contrast, if `T` is a mutable collection type then `T(x)` should always make a new
+collection (copying elements from `x`).
+
 ### Defining New Conversions
 
-To define a new conversion, simply provide a new method for `convert`. That's really all there
-is to it. For example, the method to convert a real number to a boolean is this:
+When defining a new type, initially all ways of creating it should be defined as
+constructors.
+If it becomes clear that implicit conversion would be useful, and that some
+constructors meet the above "safety" criteria, then `convert` methods can be added.
+These methods are typically quite simple, as they only need to call the appropriate
+constructor.
+Such a definition might look like this:
 
 ```julia
-convert(::Type{Bool}, x::Real) = x==0 ? false : x==1 ? true : throw(InexactError())
+convert(::Type{MyType}, x) = MyType(x)
 ```
 
 The type of the first argument of this method is a [singleton type](@ref man-singleton-types),
-`Type{Bool}`, the only instance of which is [`Bool`](@ref). Thus, this method is only invoked
-when the first argument is the type value `Bool`. Notice the syntax used for the first
+`Type{MyType}`, the only instance of which is `MyType`. Thus, this method is only invoked
+when the first argument is the type value `MyType`. Notice the syntax used for the first
 argument: the argument name is omitted prior to the `::` symbol, and only the type is given.
 This is the syntax in Julia for a function argument whose type is specified but whose value
 is never used in the function body. In this example, since the type is a singleton, there
-would never be any reason to use its value within the body. When invoked, the method
-determines whether a numeric value is true or false as a boolean,
-by comparing it to one and zero:
+would never be any reason to use its value within the body.
 
-```jldoctest
-julia> convert(Bool, 1)
-true
-
-julia> convert(Bool, 0)
-false
-
-julia> convert(Bool, 1im)
-ERROR: InexactError: convert(Bool, 0 + 1im)
-Stacktrace:
- [1] convert(::Type{Bool}, ::Complex{Int64}) at ./complex.jl:37
-
-julia> convert(Bool, 0im)
-false
-```
-
-The method signatures for conversion methods are often quite a bit more involved than this example,
-especially for parametric types. The example above is meant to be pedagogical, and is not the
-actual Julia behaviour. This is the actual implementation in Julia:
+All instances of some abstract types are by default considered "sufficiently similar"
+that a universal `convert` definition is provided in the standard library.
+For example, this definition states that it's valid to `convert` any `Number` type to
+any other by calling a 1-argument constructor:
 
 ```julia
-convert(::Type{T}, z::Complex) where {T<:Real} =
-    (imag(z) == 0 ? convert(T, real(z)) : throw(InexactError()))
+convert(::Type{T}, x::Number) where {T<:Number} = T(x)
 ```
 
-### [Case Study: Rational Conversions](@id man-rational-conversion)
-
-To continue our case study of Julia's [`Rational`](@ref) type, here are the conversions declared in
-[`rational.jl`](https://github.com/JuliaLang/julia/blob/master/base/rational.jl),
-right after the declaration of the type and its constructors:
+This means that new `Number` types only need to define constructors, since this
+definition will handle `convert` for them.
+An identity conversion is also provided to handle the case where the argument is
+already of the requested type:
 
 ```julia
-convert(::Type{Rational{T}}, x::Rational) where {T<:Integer} = Rational(convert(T,x.num),convert(T,x.den))
-convert(::Type{Rational{T}}, x::Integer) where {T<:Integer} = Rational(convert(T,x), convert(T,1))
-
-function convert(::Type{Rational{T}}, x::AbstractFloat, tol::Real) where T<:Integer
-    if isnan(x); return zero(T)//zero(T); end
-    if isinf(x); return sign(x)//zero(T); end
-    y = x
-    a = d = one(T)
-    b = c = zero(T)
-    while true
-        f = convert(T,round(y)); y -= f
-        a, b, c, d = f*a+c, f*b+d, a, b
-        if y == 0 || abs(a/b-x) <= tol
-            return a//b
-        end
-        y = 1/y
-    end
-end
-convert(rt::Type{Rational{T}}, x::AbstractFloat) where {T<:Integer} = convert(rt,x,eps(x))
-
-convert(::Type{T}, x::Rational) where {T<:AbstractFloat} = convert(T,x.num)/convert(T,x.den)
-convert(::Type{T}, x::Rational) where {T<:Integer} = div(convert(T,x.num),convert(T,x.den))
+convert(::Type{T}, x::T) where {T<:Number} = x
 ```
 
-The initial four convert methods provide conversions to rational types. The first method converts
-one type of rational to another type of rational by converting the numerator and denominator to
-the appropriate integer type. The second method does the same conversion for integers by taking
-the denominator to be 1. The third method implements a standard algorithm for approximating a
-floating-point number by a ratio of integers to within a given tolerance, and the fourth method
-applies it, using machine epsilon at the given value as the threshold. In general, one should
-have `a//b == convert(Rational{Int64}, a/b)`.
-
-The last two convert methods provide conversions from rational types to floating-point and integer
-types. To convert to floating point, one simply converts both numerator and denominator to that
-floating point type and then divides. To convert to integer, one can use the `div` operator for
-truncated integer division (rounded towards zero).
+Similar definitions exist for `AbstractString`, `AbstractArray`, and `AbstractDict`.
 
 ## Promotion
 
@@ -327,8 +316,8 @@ of rational numbers, resulting in a rational of the promotion of their respectiv
 types. The third and final rule dictates that promoting a rational with a float results in the
 same type as promoting the numerator/denominator type with the float.
 
-This small handful of promotion rules, together with the [conversion methods discussed above](@ref man-rational-conversion),
-are sufficient to make rational numbers interoperate completely naturally with all of Julia's
-other numeric types -- integers, floating-point numbers, and complex numbers. By providing appropriate
-conversion methods and promotion rules in the same manner, any user-defined numeric type can interoperate
-just as naturally with Julia's predefined numerics.
+This small handful of promotion rules, together with the type's constructors and the default
+`convert` method for numbers, are sufficient to make rational numbers interoperate completely
+naturally with all of Julia's other numeric types -- integers, floating-point numbers, and complex
+numbers. By providing appropriate conversion methods and promotion rules in the same manner, any
+user-defined numeric type can interoperate just as naturally with Julia's predefined numerics.
diff --git a/doc/src/manual/methods.md b/doc/src/manual/methods.md
index 13a92b64cc21f..927282bfec675 100644
--- a/doc/src/manual/methods.md
+++ b/doc/src/manual/methods.md
@@ -865,7 +865,7 @@ julia> p(3)
 ```
 
 This mechanism is also the key to how type constructors and closures (inner functions that refer
-to their surrounding environment) work in Julia, discussed [later in the manual](@ref constructors-and-conversion).
+to their surrounding environment) work in Julia.
 
 ## Empty generic functions
 
diff --git a/src/jltypes.c b/src/jltypes.c
index be7728eb89bd1..d8830d34c7589 100644
--- a/src/jltypes.c
+++ b/src/jltypes.c
@@ -405,6 +405,8 @@ static void flatten_type_union(jl_value_t **types, size_t n, jl_value_t **out, s
 
 STATIC_INLINE const char *datatype_module_name(jl_value_t *t)
 {
+    if (((jl_datatype_t*)t)->name->module == NULL)
+        return NULL;
     return jl_symbol_name(((jl_datatype_t*)t)->name->module->name);
 }
 
diff --git a/stdlib/Dates/src/periods.jl b/stdlib/Dates/src/periods.jl
index 1a74892e23a6d..37ea6504ab887 100644
--- a/stdlib/Dates/src/periods.jl
+++ b/stdlib/Dates/src/periods.jl
@@ -401,8 +401,13 @@ function divexact(x, y)
     return q
 end
 
+# TODO: this is needed to prevent undefined Period constructors from
+# hitting the deprecated construct-to-convert fallback.
+(::Type{T})(p::Period) where {T<:Period} = convert(T, p)::T
+
 # FixedPeriod conversions and promotion rules
-const fixedperiod_conversions = [(Week, 7), (Day, 24), (Hour, 60), (Minute, 60), (Second, 1000), (Millisecond, 1000), (Microsecond, 1000), (Nanosecond, 1)]
+const fixedperiod_conversions = [(:Week, 7), (:Day, 24), (:Hour, 60), (:Minute, 60), (:Second, 1000),
+                                 (:Millisecond, 1000), (:Microsecond, 1000), (:Nanosecond, 1)]
 for i = 1:length(fixedperiod_conversions)
     T, n = fixedperiod_conversions[i]
     N = Int64(1)
diff --git a/stdlib/Dates/test/periods.jl b/stdlib/Dates/test/periods.jl
index 85a3b05a6ba16..455d5a8116cd7 100644
--- a/stdlib/Dates/test/periods.jl
+++ b/stdlib/Dates/test/periods.jl
@@ -252,6 +252,8 @@ struct Beat <: Dates.Period
     value::Int64
 end
 
+Beat(p::Period) = Beat(Dates.toms(p) ÷ 86400)
+
 @testset "comparisons with new subtypes of Period" begin
     # https://en.wikipedia.org/wiki/Swatch_Internet_Time
     Dates.value(b::Beat) = b.value
diff --git a/stdlib/SharedArrays/src/SharedArrays.jl b/stdlib/SharedArrays/src/SharedArrays.jl
index 5f4cb9ea23310..d7b933c723087 100644
--- a/stdlib/SharedArrays/src/SharedArrays.jl
+++ b/stdlib/SharedArrays/src/SharedArrays.jl
@@ -344,15 +344,15 @@ localindices(S::SharedArray) = S.pidx > 0 ? range_1dim(S, S.pidx) : 1:0
 unsafe_convert(::Type{Ptr{T}}, S::SharedArray{T}) where {T} = unsafe_convert(Ptr{T}, sdata(S))
 unsafe_convert(::Type{Ptr{T}}, S::SharedArray   ) where {T} = unsafe_convert(Ptr{T}, sdata(S))
 
-function convert(::Type{SharedArray}, A::Array)
+function SharedArray(A::Array)
     S = SharedArray{eltype(A),ndims(A)}(size(A))
     copyto!(S, A)
 end
-function convert(::Type{SharedArray{T}}, A::Array) where T
+function SharedArray{T}(A::Array) where T
     S = SharedArray{T,ndims(A)}(size(A))
     copyto!(S, A)
 end
-function convert(::Type{SharedArray{TS,N}}, A::Array{TA,N}) where {TS,TA,N}
+function SharedArray{TS,N}(A::Array{TA,N}) where {TS,TA,N}
     S = SharedArray{TS,ndims(A)}(size(A))
     copyto!(S, A)
 end
@@ -491,7 +491,7 @@ function show(io::IO, mime::MIME"text/plain", S::SharedArray)
     end
 end
 
-convert(::Type{Array}, S::SharedArray) = S.s
+Array(S::SharedArray) = S.s
 
 # pass through getindex and setindex! - unlike DArrays, these always work on the complete array
 getindex(S::SharedArray, i::Real) = getindex(S.s, i)
diff --git a/stdlib/SuiteSparse/src/cholmod.jl b/stdlib/SuiteSparse/src/cholmod.jl
index 2c4a7ba535ebd..22a7f88baa43d 100644
--- a/stdlib/SuiteSparse/src/cholmod.jl
+++ b/stdlib/SuiteSparse/src/cholmod.jl
@@ -345,6 +345,7 @@ mutable struct Factor{Tv} <: Factorization{Tv}
     end
 end
 Factor(p::Ptr{C_Factor{Tv}}) where {Tv<:VTypes} = Factor{Tv}(p)
+Factor(x::Factor) = x
 
 # All pointer loads should be checked to make sure that SuiteSparse is not called with
 # a C_NULL pointer which could cause a segfault. Pointers are set to null
@@ -819,7 +820,7 @@ get_perm(FC::FactorComponent) = get_perm(Factor(FC))
 #########################
 
 # Convertion/construction
-function convert(::Type{Dense{T}}, A::StridedVecOrMat) where T<:VTypes
+function Dense{T}(A::StridedVecOrMat) where T<:VTypes
     d = allocate_dense(size(A, 1), size(A, 2), stride(A, 2), T)
     s = unsafe_load(d.p)
     for i in eachindex(A)
@@ -827,11 +828,11 @@ function convert(::Type{Dense{T}}, A::StridedVecOrMat) where T<:VTypes
     end
     d
 end
-function convert(::Type{Dense}, A::StridedVecOrMat)
+function Dense(A::StridedVecOrMat)
     T = promote_type(eltype(A), Float64)
-    return convert(Dense{T}, A)
+    return Dense{T}(A)
 end
-convert(::Type{Dense}, A::Sparse) = sparse_to_dense(A)
+Dense(A::Sparse) = sparse_to_dense(A)
 
 # This constructior assumes zero based colptr and rowval
 function Sparse(m::Integer, n::Integer,
@@ -913,9 +914,8 @@ function Sparse(A::SparseMatrixCSC{Tv,SuiteSparse_long}, stype::Integer) where T
 end
 
 # convert SparseVectors into CHOLMOD Sparse types through a mx1 CSC matrix
-convert(::Type{Sparse}, A::SparseVector{<:VTypes,SuiteSparse_long}) =
-    convert(Sparse, convert(SparseMatrixCSC, A))
-function convert(::Type{Sparse}, A::SparseMatrixCSC{<:VTypes,<:ITypes})
+Sparse(A::SparseVector{<:VTypes,SuiteSparse_long}) = Sparse(SparseMatrixCSC(A))
+function Sparse(A::SparseMatrixCSC{<:VTypes,<:ITypes})
     o = Sparse(A, 0)
     # check if array is symmetric and change stype if it is
     if ishermitian(o)
@@ -923,15 +923,15 @@ function convert(::Type{Sparse}, A::SparseMatrixCSC{<:VTypes,<:ITypes})
     end
     o
 end
-convert(::Type{Sparse}, A::SparseMatrixCSC{Complex{Float32},<:ITypes}) =
-    convert(Sparse, convert(SparseMatrixCSC{Complex{Float64},SuiteSparse_long}, A))
-convert(::Type{Sparse}, A::Symmetric{Float64,SparseMatrixCSC{Float64,SuiteSparse_long}}) =
+Sparse(A::SparseMatrixCSC{Complex{Float32},<:ITypes}) =
+    Sparse(SparseMatrixCSC{Complex{Float64},SuiteSparse_long}(A))
+Sparse(A::Symmetric{Float64,SparseMatrixCSC{Float64,SuiteSparse_long}}) =
     Sparse(A.data, A.uplo == 'L' ? -1 : 1)
 # The convert method for Hermitian is very similar to the general convert method, but we need to
 # remove any non real elements in the diagonal because, in contrast to BLAS/LAPACK these are not
 # ignored by CHOLMOD. If even tiny imaginary parts are present CHOLMOD will fail with a non-positive
 # definite/zero pivot error.
-function convert(::Type{Sparse}, AH::Hermitian{Tv,SparseMatrixCSC{Tv,SuiteSparse_long}}) where {Tv<:VTypes}
+function Sparse(AH::Hermitian{Tv,SparseMatrixCSC{Tv,SuiteSparse_long}}) where {Tv<:VTypes}
     A = AH.data
 
     # Here we allocate a Symmetric/Hermitian CHOLMOD.Sparse matrix so we only need to copy
@@ -955,23 +955,21 @@ function convert(::Type{Sparse}, AH::Hermitian{Tv,SparseMatrixCSC{Tv,SuiteSparse
 
     return o
 end
-function convert(::Type{Sparse},
-                 A::Union{SparseMatrixCSC{BigFloat,Ti},
-                          Symmetric{BigFloat,SparseMatrixCSC{BigFloat,Ti}},
-                          Hermitian{Complex{BigFloat},SparseMatrixCSC{Complex{BigFloat},Ti}}},
-                 args...) where Ti<:ITypes
-    throw(MethodError(convert, (Sparse, A)))
+function Sparse(A::Union{SparseMatrixCSC{BigFloat,Ti},
+                         Symmetric{BigFloat,SparseMatrixCSC{BigFloat,Ti}},
+                         Hermitian{Complex{BigFloat},SparseMatrixCSC{Complex{BigFloat},Ti}}},
+                args...) where Ti<:ITypes
+    throw(MethodError(Sparse, (A,)))
 end
-function convert(::Type{Sparse},
-    A::Union{SparseMatrixCSC{T,Ti},
-             Symmetric{T,SparseMatrixCSC{T,Ti}},
-             Hermitian{T,SparseMatrixCSC{T,Ti}}},
-    args...) where T where Ti<:ITypes
-    return Sparse(convert(AbstractMatrix{promote_type(Float64, T)}, A), args...)
+function Sparse(A::Union{SparseMatrixCSC{T,Ti},
+                         Symmetric{T,SparseMatrixCSC{T,Ti}},
+                         Hermitian{T,SparseMatrixCSC{T,Ti}}},
+                args...) where T where Ti<:ITypes
+    return Sparse(AbstractMatrix{promote_type(Float64, T)}(A), args...)
 end
 
 # Useful when reading in files, but not type stable
-function convert(::Type{Sparse}, p::Ptr{C_SparseVoid})
+function Sparse(p::Ptr{C_SparseVoid})
     if p == C_NULL
         throw(ArgumentError("sparse matrix construction failed for " *
             "unknown reasons. Please submit a bug report."))
@@ -1016,8 +1014,8 @@ function convert(::Type{Sparse}, p::Ptr{C_SparseVoid})
     return Sparse(convert(Ptr{C_Sparse{Tv}}, p))
 end
 
-convert(::Type{Sparse}, A::Dense) = dense_to_sparse(A, SuiteSparse_long)
-convert(::Type{Sparse}, L::Factor) = factor_to_sparse!(copy(L))
+Sparse(A::Dense) = dense_to_sparse(A, SuiteSparse_long)
+Sparse(L::Factor) = factor_to_sparse!(copy(L))
 function Sparse(filename::String)
     open(filename) do f
         return read_sparse(f, SuiteSparse_long)
@@ -1025,7 +1023,7 @@ function Sparse(filename::String)
 end
 
 ## convertion back to base Julia types
-function convert(::Type{Matrix{T}}, D::Dense{T}) where T
+function Matrix{T}(D::Dense{T}) where T
     s = unsafe_load(D.p)
     a = Matrix{T}(uninitialized, s.nrow, s.ncol)
     copyto!(a, D)
@@ -1053,16 +1051,16 @@ function _copy!(dest::AbstractArray, D::Dense)
     end
     dest
 end
-convert(::Type{Matrix}, D::Dense{T}) where {T} = convert(Matrix{T}, D)
-function convert(::Type{Vector{T}}, D::Dense{T}) where T
+Matrix(D::Dense{T}) where {T} = Matrix{T}(D)
+function Vector{T}(D::Dense{T}) where T
     if size(D, 2) > 1
         throw(DimensionMismatch("input must be a vector but had $(size(D, 2)) columns"))
     end
     copyto!(Vector{T}(uninitialized, size(D, 1)), D)
 end
-convert(::Type{Vector}, D::Dense{T}) where {T} = convert(Vector{T}, D)
+Vector(D::Dense{T}) where {T} = Vector{T}(D)
 
-function convert(::Type{SparseMatrixCSC{Tv,SuiteSparse_long}}, A::Sparse{Tv}) where Tv
+function SparseMatrixCSC{Tv,SuiteSparse_long}(A::Sparse{Tv}) where Tv
     s = unsafe_load(A.p)
     if s.stype != 0
         throw(ArgumentError("matrix has stype != 0. Convert to matrix " *
@@ -1080,7 +1078,7 @@ function convert(::Type{SparseMatrixCSC{Tv,SuiteSparse_long}}, A::Sparse{Tv}) wh
         return B
     end
 end
-function convert(::Type{Symmetric{Float64,SparseMatrixCSC{Float64,SuiteSparse_long}}}, A::Sparse{Float64})
+function (::Type{Symmetric{Float64,SparseMatrixCSC{Float64,SuiteSparse_long}}})(A::Sparse{Float64})
     s = unsafe_load(A.p)
     if !issymmetric(A)
         throw(ArgumentError("matrix is not symmetric"))
@@ -1097,7 +1095,7 @@ function convert(::Type{Symmetric{Float64,SparseMatrixCSC{Float64,SuiteSparse_lo
         return B
     end
 end
-function convert(::Type{Hermitian{Tv,SparseMatrixCSC{Tv,SuiteSparse_long}}}, A::Sparse{Tv}) where Tv<:VTypes
+function Hermitian{Tv,SparseMatrixCSC{Tv,SuiteSparse_long}}(A::Sparse{Tv}) where Tv<:VTypes
     s = unsafe_load(A.p)
     if !ishermitian(A)
         throw(ArgumentError("matrix is not Hermitian"))
@@ -1117,16 +1115,16 @@ end
 function sparse(A::Sparse{Float64}) # Notice! Cannot be type stable because of stype
     s = unsafe_load(A.p)
     if s.stype == 0
-        return convert(SparseMatrixCSC{Float64,SuiteSparse_long}, A)
+        return SparseMatrixCSC{Float64,SuiteSparse_long}(A)
     end
-    return convert(Symmetric{Float64,SparseMatrixCSC{Float64,SuiteSparse_long}}, A)
+    return Symmetric{Float64,SparseMatrixCSC{Float64,SuiteSparse_long}}(A)
 end
 function sparse(A::Sparse{Complex{Float64}}) # Notice! Cannot be type stable because of stype
     s = unsafe_load(A.p)
     if s.stype == 0
-        return convert(SparseMatrixCSC{Complex{Float64},SuiteSparse_long}, A)
+        return SparseMatrixCSC{Complex{Float64},SuiteSparse_long}(A)
     end
-    return convert(Hermitian{Complex{Float64},SparseMatrixCSC{Complex{Float64},SuiteSparse_long}}, A)
+    return Hermitian{Complex{Float64},SparseMatrixCSC{Complex{Float64},SuiteSparse_long}}(A)
 end
 function sparse(F::Factor)
     s = unsafe_load(pointer(F))
@@ -1665,10 +1663,10 @@ end
 SparseVecOrMat{Tv,Ti} = Union{SparseVector{Tv,Ti}, SparseMatrixCSC{Tv,Ti}}
 
 function (\)(L::FactorComponent, b::Vector)
-    reshape(convert(Matrix, L\Dense(b)), length(b))
+    reshape(Matrix(L\Dense(b)), length(b))
 end
 function (\)(L::FactorComponent, B::Matrix)
-    convert(Matrix, L\Dense(B))
+    Matrix(L\Dense(B))
 end
 function (\)(L::FactorComponent, B::SparseVecOrMat)
     sparse(L\Sparse(B,0))
@@ -1682,14 +1680,14 @@ end
 # Likewise the two following explicit Vector and Matrix defs (rather than a single VecOrMat)
 (\)(L::Factor{T}, B::Vector{Complex{T}}) where {T<:Float64} = complex.(L\real(B), L\imag(B))
 (\)(L::Factor{T}, B::Matrix{Complex{T}}) where {T<:Float64} = complex.(L\real(B), L\imag(B))
-(\)(L::Factor{T}, b::StridedVector) where {T<:VTypes} = Vector(L\convert(Dense{T}, b))
-(\)(L::Factor{T}, B::StridedMatrix) where {T<:VTypes} = Matrix(L\convert(Dense{T}, B))
+(\)(L::Factor{T}, b::StridedVector) where {T<:VTypes} = Vector(L\Dense{T}(b))
+(\)(L::Factor{T}, B::StridedMatrix) where {T<:VTypes} = Matrix(L\Dense{T}(B))
 (\)(L::Factor, B::Sparse) = spsolve(CHOLMOD_A, L, B)
 # When right hand side is sparse, we have to ensure that the rhs is not marked as symmetric.
 (\)(L::Factor, B::SparseVecOrMat) = sparse(spsolve(CHOLMOD_A, L, Sparse(B, 0)))
 
 \(adjL::Adjoint{<:Any,<:Factor}, B::Dense) = (L = adjL.parent; solve(CHOLMOD_A, L, B))
-\(adjL::Adjoint{<:Any,<:Factor}, B::VecOrMat) = (L = adjL.parent; convert(Matrix, solve(CHOLMOD_A, L, Dense(B))))
+\(adjL::Adjoint{<:Any,<:Factor}, B::VecOrMat) = (L = adjL.parent; Matrix(solve(CHOLMOD_A, L, Dense(B))))
 \(adjL::Adjoint{<:Any,<:Factor}, B::Sparse) = (L = adjL.parent; spsolve(CHOLMOD_A, L, B))
 \(adjL::Adjoint{<:Any,<:Factor}, B::SparseVecOrMat) = (L = adjL.parent; \(Adjoint(L), Sparse(B)))
 
@@ -1706,7 +1704,7 @@ function \(A::RealHermSymComplexHermF64SSL, B::StridedVecOrMat)
         if issuccess(F)
             return \(F, B)
         else
-            return \(lufact(convert(SparseMatrixCSC{eltype(A), SuiteSparse_long}, A)), B)
+            return \(lufact(SparseMatrixCSC{eltype(A), SuiteSparse_long}(A)), B)
         end
     end
 end
@@ -1720,7 +1718,7 @@ function \(adjA::Adjoint{<:Any,<:RealHermSymComplexHermF64SSL}, B::StridedVecOrM
         if issuccess(F)
             return \(Adjoint(F), B)
         else
-            return \(Adjoint(lufact(convert(SparseMatrixCSC{eltype(A), SuiteSparse_long}, A))), B)
+            return \(Adjoint(lufact(SparseMatrixCSC{eltype(A), SuiteSparse_long}(A))), B)
         end
     end
 end
diff --git a/stdlib/Test/src/Test.jl b/stdlib/Test/src/Test.jl
index e3383937910d5..bdac989c92133 100644
--- a/stdlib/Test/src/Test.jl
+++ b/stdlib/Test/src/Test.jl
@@ -1449,7 +1449,6 @@ end
 for (G, A) in ((GenericSet, AbstractSet),
                (GenericDict, AbstractDict))
     @eval begin
-        Base.convert(::Type{$G}, s::$A) = $G(s)
         Base.done(s::$G, state) = done(s.s, state)
         Base.next(s::$G, state) = next(s.s, state)
     end
diff --git a/test/abstractarray.jl b/test/abstractarray.jl
index 5a761c51249b2..5b1ec4bd6cf89 100644
--- a/test/abstractarray.jl
+++ b/test/abstractarray.jl
@@ -199,9 +199,9 @@ end
 T24Linear(::Type{T}, dims::Int...) where T = T24Linear(T, dims)
 T24Linear(::Type{T}, dims::NTuple{N,Int}) where {T,N} = T24Linear{T,N,dims}()
 
-Base.convert(::Type{T24Linear     }, X::AbstractArray{T,N}) where {T,N  } = convert(T24Linear{T,N}, X)
-Base.convert(::Type{T24Linear{T  }}, X::AbstractArray{_,N}) where {T,N,_} = convert(T24Linear{T,N}, X)
-Base.convert(::Type{T24Linear{T,N}}, X::AbstractArray     ) where {T,N  } = T24Linear{T,N,size(X)}(X...)
+T24Linear(     X::AbstractArray{T,N}) where {T,N  } = T24Linear{T,N}(X)
+T24Linear{T  }(X::AbstractArray{_,N}) where {T,N,_} = T24Linear{T,N}(X)
+T24Linear{T,N}(X::AbstractArray     ) where {T,N  } = T24Linear{T,N,size(X)}(X...)
 
 Base.size(::T24Linear{T,N,dims}) where {T,N,dims} = dims
 import Base: IndexLinear
@@ -217,10 +217,10 @@ end
 TSlow(::Type{T}, dims::Int...) where {T} = TSlow(T, dims)
 TSlow(::Type{T}, dims::NTuple{N,Int}) where {T,N} = TSlow{T,N}(Dict{NTuple{N,Int}, T}(), dims)
 
-Base.convert(::Type{TSlow{T,N}}, X::TSlow{T,N})         where {T,N  } = X
-Base.convert(::Type{TSlow     }, X::AbstractArray{T,N}) where {T,N  } = convert(TSlow{T,N}, X)
-Base.convert(::Type{TSlow{T  }}, X::AbstractArray{_,N}) where {T,N,_} = convert(TSlow{T,N}, X)
-Base.convert(::Type{TSlow{T,N}}, X::AbstractArray     ) where {T,N  } = begin
+TSlow{T,N}(X::TSlow{T,N})         where {T,N  } = X
+TSlow(     X::AbstractArray{T,N}) where {T,N  } = TSlow{T,N}(X)
+TSlow{T  }(X::AbstractArray{_,N}) where {T,N,_} = TSlow{T,N}(X)
+TSlow{T,N}(X::AbstractArray     ) where {T,N  } = begin
     A = TSlow(T, size(X))
     for I in CartesianIndices(size(X))
         A[I.I...] = X[I.I...]
diff --git a/test/arrayops.jl b/test/arrayops.jl
index 547f7bf2f65b5..6a8f47d22712b 100644
--- a/test/arrayops.jl
+++ b/test/arrayops.jl
@@ -2172,7 +2172,7 @@ end
 
 Base.TypeArithmetic(::Type{F21666{T}}) where {T} = T()
 Base.:+(x::F, y::F) where {F <: F21666} = F(x.x + y.x)
-Base.convert(::Type{Float64}, x::F21666) = Float64(x.x)
+Float64(x::F21666) = Float64(x.x)
 @testset "Exactness of cumsum # 21666" begin
     # test that cumsum uses more stable algorithm
     # for types with unknown/rounding arithmetic
diff --git a/test/choosetests.jl b/test/choosetests.jl
index 7cf2f45eb7749..aea130dd8e9f0 100644
--- a/test/choosetests.jl
+++ b/test/choosetests.jl
@@ -136,14 +136,6 @@ function choosetests(choices = [])
         prepend!(tests, linalgtests)
     end
 
-    # do ambiguous first to avoid failing if ambiguities are introduced by other tests
-    if "ambiguous" in skip_tests
-        filter!(x -> x != "ambiguous", tests)
-    elseif "ambiguous" in tests
-        filter!(x -> x != "ambiguous", tests)
-        prepend!(tests, ["ambiguous"])
-    end
-
     net_required_for = ["socket", "stdlib", "libgit2"]
     net_on = true
     try
@@ -169,6 +161,14 @@ function choosetests(choices = [])
         prepend!(tests, STDLIBS)
     end
 
+    # do ambiguous first to avoid failing if ambiguities are introduced by other tests
+    if "ambiguous" in skip_tests
+        filter!(x -> x != "ambiguous", tests)
+    elseif "ambiguous" in tests
+        filter!(x -> x != "ambiguous", tests)
+        prepend!(tests, ["ambiguous"])
+    end
+
     if startswith(string(Sys.ARCH), "arm")
         # Remove profile from default tests on ARM since it currently segfaults
         # Allow explicitly adding it for testing
diff --git a/test/dimensionful.jl b/test/dimensionful.jl
index bb3b5ac2043af..5c526c17e93ff 100644
--- a/test/dimensionful.jl
+++ b/test/dimensionful.jl
@@ -11,12 +11,9 @@ struct Furlong{p,T<:Number} <: Number
     Furlong{p,T}(x::Furlong{p}) where {p,T} = new(x.val)
 end
 Furlong(x::T) where {T<:Number} = Furlong{1,T}(x)
-(::Type{T})(x::Furlong{p,T}) where {p,T} = x.val
+(::Type{T})(x::Furlong) where {T<:Number} = T(x.val)
 Furlong{p}(v::Number) where {p} = Furlong{p,typeof(v)}(v)
-Base.convert(::Type{Furlong{p,T}}, x::Furlong{p,S}) where {T,p,S} = Furlong{p,T}(convert(T,x.val))
-Base.convert(::Type{Furlong{0,T}}, x::Furlong{0}) where {T} = Furlong{0,T}(convert(T, x.val))
-Base.convert(::Type{T}, x::Furlong{0}) where {T<:Number} = convert(T, x.val)
-Base.convert(::Type{Furlong{0,T}}, x::Number) where {T} = Furlong{0,T}(convert(T, x))
+Furlong{p,T}(x::Furlong{p,S}) where {T,p,S} = Furlong{p,T}(T(x.val))
 
 Base.promote_type(::Type{Furlong{p,T}}, ::Type{Furlong{p,S}}) where {p,T,S} =
     (Base.@_pure_meta; Furlong{p,promote_type(T,S)})
diff --git a/test/enums.jl b/test/enums.jl
index a4cd797ce9035..068aafff29e49 100644
--- a/test/enums.jl
+++ b/test/enums.jl
@@ -36,19 +36,19 @@ end
 @test_throws MethodError Fruit(0.0)
 @test typemin(Fruit) == apple
 @test typemax(Fruit) == kiwi
-@test convert(Fruit,0) == apple
-@test convert(Fruit,1) == orange
-@test convert(Fruit,2) == kiwi
-@test_throws ArgumentError convert(Fruit,3)
-@test_throws ArgumentError convert(Fruit,-1)
-@test convert(UInt8,apple) === 0x00
-@test convert(UInt16,orange) === 0x0001
-@test convert(UInt128,kiwi) === 0x00000000000000000000000000000002
-@test typeof(convert(BigInt,apple)) <: BigInt
-@test convert(BigInt,apple) == 0
-@test convert(Bool,apple) == false
-@test convert(Bool,orange) == true
-@test_throws InexactError convert(Bool,kiwi)
+@test Fruit(0) == apple
+@test Fruit(1) == orange
+@test Fruit(2) == kiwi
+@test_throws ArgumentError Fruit(3)
+@test_throws ArgumentError Fruit(-1)
+@test UInt8(apple) === 0x00
+@test UInt16(orange) === 0x0001
+@test UInt128(kiwi) === 0x00000000000000000000000000000002
+@test typeof(BigInt(apple)) <: BigInt
+@test BigInt(apple) == 0
+@test Bool(apple) == false
+@test Bool(orange) == true
+@test_throws InexactError Bool(kiwi)
 @test instances(Fruit) == (apple, orange, kiwi)
 
 f(x::Fruit) = "hey, I'm a Fruit"
@@ -76,7 +76,7 @@ end
 @enum Negative _neg1=-1 _neg2=-2
 @test Int(_neg1) === -1
 @test Int(_neg2) === -2
-@test_throws InexactError convert(UInt8, _neg1)
+@test_throws InexactError UInt8(_neg1)
 @enum Negative2 _neg5=-5 _neg4 _neg3
 @test Int(_neg5) === -5
 @test Int(_neg4) === -4
@@ -98,7 +98,7 @@ end
 # other Integer types of enum members
 @enum Test3::UInt8 _one_Test3=0x01 _two_Test3=0x02 _three_Test3=0x03
 @test Test3.size == 1
-@test convert(UInt8, _one_Test3) === 0x01
+@test UInt8(_one_Test3) === 0x01
 @test length(instances(Test3)) == 3
 
 @enum Test4::UInt16 _one_Test4=0x01 _two_Test4=0x0002 _three_Test4=0x03
@@ -109,7 +109,7 @@ end
 
 @enum Test6::UInt128 _one_Test6=0x00000000000000000000000000000001 _two_Test6=0x00000000000000000000000000000002
 @test Test6.size == 16
-@test typeof(convert(Integer, _one_Test6)) == UInt128
+@test typeof(Integer(_one_Test6)) == UInt128
 
 # enum values must be integers
 @test_throws ArgumentError("invalid value for Enum Test7, _zero = \"zero\"=zero; values must be integers") @macrocall(@enum Test7 _zero="zero")
diff --git a/test/file.jl b/test/file.jl
index e5db8bbf3ab7e..4c51cf2616b55 100644
--- a/test/file.jl
+++ b/test/file.jl
@@ -829,7 +829,7 @@ let f = open(file, "w")
     write(f, "Hello, world!")
     close(f)
     f = open(file, "r")
-    test_LibcFILE(convert(Libc.FILE, f))
+    test_LibcFILE(Libc.FILE(f))
     close(f)
     if Sys.iswindows()
         f = RawFD(ccall(:_open, Cint, (Cstring, Cint), file, Base.Filesystem.JL_O_RDONLY))
diff --git a/test/ranges.jl b/test/ranges.jl
index 75eca6ad821fa..db15dc9e98821 100644
--- a/test/ranges.jl
+++ b/test/ranges.jl
@@ -1175,8 +1175,8 @@ Base.isless(x, y::NotReal) = isless(x, y.val)
 isdefined(Main, :TestHelpers) || @eval Main include("TestHelpers.jl")
 using Main.TestHelpers.Furlong
 @testset "dimensional correctness" begin
-    @test_throws MethodError collect(Furlong(2):Furlong(10)) # step size is ambiguous
-    @test_throws MethodError range(Furlong(2), 9) # step size is ambiguous
+    @test length(collect(Furlong(2):Furlong(10))) == 9
+    @test length(range(Furlong(2), 9)) == 9
     @test collect(Furlong(2):Furlong(1):Furlong(10)) == collect(range(Furlong(2),Furlong(1),9)) == Furlong.(2:10)
     @test collect(Furlong(1.0):Furlong(0.5):Furlong(10.0)) ==
           collect(Furlong(1):Furlong(0.5):Furlong(10)) == Furlong.(1:0.5:10)
diff --git a/test/strings/basic.jl b/test/strings/basic.jl
index 687d64ba56a9d..092828c6c4c76 100644
--- a/test/strings/basic.jl
+++ b/test/strings/basic.jl
@@ -302,7 +302,7 @@ end
     end
     let s = Base.Unicode.normalize("tést",:NFKC)
         @test unsafe_string(Base.unsafe_convert(Cstring, Base.cconvert(Cstring, s))) == s
-        @test unsafe_string(convert(Cstring, Symbol(s))) == s
+        @test unsafe_string(Base.unsafe_convert(Cstring, Symbol(s))) == s
     end
     @test_throws ArgumentError Base.unsafe_convert(Cstring, Base.cconvert(Cstring, "ba\0d"))
 
diff --git a/test/version.jl b/test/version.jl
index f1e94fd0df477..e45639fe16c69 100644
--- a/test/version.jl
+++ b/test/version.jl
@@ -82,15 +82,15 @@ io = IOBuffer()
 show(io,v"4.3.2+1.a")
 @test length(String(take!(io))) == 12
 
-# conversion from Int
-@test convert(VersionNumber, 2) == v"2.0.0"
+# construction from Int
+@test VersionNumber(2) == v"2.0.0"
 
-# conversion from Tuple
-@test convert(VersionNumber, (2,)) == v"2.0.0"
-@test convert(VersionNumber, (3, 2)) == v"3.2.0"
+# construction from Tuple
+@test VersionNumber((2,)) == v"2.0.0"
+@test VersionNumber((3, 2)) == v"3.2.0"
 
-# conversion from AbstractString
-@test convert(VersionNumber, "4.3.2+1.a") == v"4.3.2+1.a"
+# construction from AbstractString
+@test VersionNumber("4.3.2+1.a") == v"4.3.2+1.a"
 
 # typemin and typemax
 @test typemin(VersionNumber) == v"0-"