diff --git a/Project.toml b/Project.toml
index aed8f7094..7f29129c3 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "Compat"
 uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
-version = "3.36.0"
+version = "3.37.0"
 
 [deps]
 Base64 = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
diff --git a/README.md b/README.md
index 6f14b2385..dec822bea 100644
--- a/README.md
+++ b/README.md
@@ -54,6 +54,10 @@ changes in `julia`.
 
 ## Supported features
 
+* `Compat.@inline` and `Compat.@noinline` can be used at function callsites to encourage the compiler to (not) inline the function calls on Julia versions that support these features, and otherwise do not have any effects ([#41312]) (since Compat 3.37)
+
+* `Compat.@inline` and `Compat.@noinline` can be used within function body to hint to the compiler the inlineability of the defined function ([#41312]) (since Compat 3.37)
+
 * `Compat.@constprop :aggressive ex` and `Compat.@constprop :none ex` allow control over constant-propagation during inference on Julia versions that support this feature, and otherwise just pass back `ex`. ([#42125]) (since Compat 3.36)
 
 * `Returns(value)` returns `value` for any arguments ([#39794]) (since Compat 3.35)
@@ -276,3 +280,5 @@ Note that you should specify the correct minimum version for `Compat` in the
 [#34331]: https://github.com/JuliaLang/julia/pull/34331
 [#39794]: https://github.com/JuliaLang/julia/pull/39794
 [#42125]: https://github.com/JuliaLang/julia/pull/42125
+[#41312]: https://github.com/JuliaLang/julia/pull/41312
+[#41328]: https://github.com/JuliaLang/julia/pull/41328
diff --git a/src/Compat.jl b/src/Compat.jl
index b88961e31..250af0a8a 100644
--- a/src/Compat.jl
+++ b/src/Compat.jl
@@ -8,6 +8,50 @@ using LinearAlgebra: Adjoint, Diagonal, Transpose, UniformScaling, RealHermSymCo
 
 include("compatmacro.jl")
 
+# NOTE these `@inline` and `@noinline` definitions overwrite the definitions implicitly
+# imported from Base and so should happen before any usages of them within this module
+
+# https://github.com/JuliaLang/julia/pull/41312: `@inline`/`@noinline` annotations within a function body
+@static if !hasmethod(getfield(Base, Symbol("@inline")), (LineNumberNode,Module))
+    macro inline()   Expr(:meta, :inline)   end
+    macro noinline() Expr(:meta, :noinline) end
+end
+
+# https://github.com/JuliaLang/julia/pull/41328: callsite annotations of inlining
+@static if !isdefined(Base, :annotate_meta_def_or_block)
+    macro inline(ex)   annotate_meta_def_or_nothing(ex, :inline)   end
+    macro noinline(ex) annotate_meta_def_or_nothing(ex, :noinline) end
+    function annotate_meta_def_or_nothing(@nospecialize(ex), meta::Symbol)
+        inner = unwrap_macrocalls(ex)
+        if is_function_def(inner)
+            # annotation on a definition
+            return esc(Base.pushmeta!(ex, meta))
+        else
+            # do nothing
+            return esc(ex)
+        end
+    end
+    unwrap_macrocalls(@nospecialize(x)) = x
+    function unwrap_macrocalls(ex::Expr)
+        inner = ex
+        while inner.head === :macrocall
+            inner = inner.args[end]::Expr
+        end
+        return inner
+    end
+    is_function_def(@nospecialize(ex)) =
+        return Meta.isexpr(ex, :function) || is_short_function_def(ex) || Meta.isexpr(ex, :->)
+    function is_short_function_def(@nospecialize(ex))
+        Meta.isexpr(ex, :(=)) || return false
+        while length(ex.args) >= 1 && isa(ex.args[1], Expr)
+            (ex.args[1].head === :call) && return true
+            (ex.args[1].head === :where || ex.args[1].head === :(::)) || return false
+            ex = ex.args[1]
+        end
+        return false
+    end
+end
+
 # https://github.com/JuliaLang/julia/pull/29440
 if VERSION < v"1.1.0-DEV.389"
     Base.:(:)(I::CartesianIndex{N}, J::CartesianIndex{N}) where N =
diff --git a/test/runtests.jl b/test/runtests.jl
index 00c934bda..e8bff1b94 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1171,3 +1171,44 @@ end
     )
     @test aggf("hi") == nonef("hi") == :hi
 end
+
+# https://github.com/JuliaLang/julia/pull/41312
+@testset "`@inline`/`@noinline` annotations within a function body" begin
+    callf(f, args...) = f(args...)
+    function foo1(a)
+        Compat.@inline
+        sum(sincos(a))
+    end
+    foo2(a) = (Compat.@inline; sum(sincos(a)))
+    foo3(a) = callf(a) do a
+        Compat.@inline
+        sum(sincos(a))
+    end
+    function foo4(a)
+        Compat.@noinline
+        sum(sincos(a))
+    end
+    foo5(a) = (Compat.@noinline; sum(sincos(a)))
+    foo6(a) = callf(a) do a
+        Compat.@noinline
+        sum(sincos(a))
+    end
+
+    @test foo1(42) == foo2(42) == foo3(42) == foo4(42) == foo5(42) == foo6(42)
+end
+
+# https://github.com/JuliaLang/julia/pull/41328
+@testset "callsite annotations of inlining" begin
+    function foo1(a)
+        Compat.@inline begin
+            return sum(sincos(a))
+        end
+    end
+    function foo2(a)
+        Compat.@noinline begin
+            return sum(sincos(a))
+        end
+    end
+    
+    @test foo1(42) == foo2(42)
+end