diff --git a/Project.toml b/Project.toml
index a0abec5197..229ec62161 100644
--- a/Project.toml
+++ b/Project.toml
@@ -8,12 +8,12 @@ BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 Unicode = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
 julia = "1"
 
 [extras]
-Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Test"]
+test = []
diff --git a/docs/src/apireference.md b/docs/src/apireference.md
index d46b9be883..2a592ea5f3 100644
--- a/docs/src/apireference.md
+++ b/docs/src/apireference.md
@@ -251,6 +251,7 @@ Semicontinuous
 Semiinteger
 SOS1
 SOS2
+IndicatorSet
 ```
 
 Functions for getting and setting properties of sets.
diff --git a/src/Test/intlinear.jl b/src/Test/intlinear.jl
index 89368d217b..26c7b2b311 100644
--- a/src/Test/intlinear.jl
+++ b/src/Test/intlinear.jl
@@ -356,9 +356,242 @@ function knapsacktest(model::MOI.ModelLike, config::TestConfig)
     end
 end
 
+function indicator1_test(model::MOI.ModelLike, config::TestConfig)
+    atol = config.atol
+    rtol = config.rtol
+    # linear problem with indicator constraint
+    # max  2x1 + 3x2
+    # s.t. x1 + x2 <= 10
+    #      z1 ==> x2 <= 8
+    #      z2 ==> x2 + x1/5 <= 9
+    #      z1 + z2 >= 1
+
+    MOI.empty!(model)
+    @test MOI.is_empty(model)
+
+    @test MOI.supports(model, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}())
+    @test MOI.supports(model, MOI.ObjectiveSense())
+    @test MOI.supports_constraint(model, MOI.SingleVariable, MOI.ZeroOne)
+    @test MOI.supports_constraint(model, MOI.SingleVariable, MOI.Interval{Float64})
+    @test MOI.supports_constraint(model, MOI.ScalarAffineFunction{Float64}, MOI.Interval{Float64})
+    @test MOI.supports_constraint(model, MOI.VectorAffineFunction{Float64}, MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE, MOI.LessThan{Float64}})
+    x1 = MOI.add_variable(model)
+    x2 = MOI.add_variable(model)
+    z1 = MOI.add_variable(model)
+    z2 = MOI.add_variable(model)
+    MOI.add_constraint(model, z1, MOI.ZeroOne())
+    MOI.add_constraint(model, z2, MOI.ZeroOne())
+    f1 = MOI.VectorAffineFunction(
+        [MOI.VectorAffineTerm(1, MOI.ScalarAffineTerm(1.0, z1)),
+         MOI.VectorAffineTerm(2, MOI.ScalarAffineTerm(1.0, x2)),
+        ],
+        [0.0, 0.0]
+    )
+    iset1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
+    MOI.add_constraint(model, f1, iset1)
+
+    f2 = MOI.VectorAffineFunction(
+        [MOI.VectorAffineTerm(1, MOI.ScalarAffineTerm(1.0, z2)),
+         MOI.VectorAffineTerm(2, MOI.ScalarAffineTerm(0.2, x1)),
+         MOI.VectorAffineTerm(2, MOI.ScalarAffineTerm(1.0, x2)),
+        ],
+        [0.0, 0.0],
+    )
+    iset2 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
+
+    MOI.add_constraint(model, f2, iset2)
+
+    # Additional regular constraint.
+    MOI.add_constraint(model,
+        MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(1.0, x1), MOI.ScalarAffineTerm(1.0, x2)], 0.0),
+        MOI.LessThan(10.0),
+    )
+
+    # Disjunction z1 ⋁ z2
+    MOI.add_constraint(model,
+        MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(1.0, z1), MOI.ScalarAffineTerm(1.0, z2)], 0.0),
+        MOI.GreaterThan(1.0),
+    )
+
+    MOI.set(model, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}(),
+        MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([2.0, 3.0], [x1, x2]), 0.0)
+    )
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
+
+    if config.solve
+        @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
+
+        MOI.optimize!(model)
+
+        @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMAL
+        @test MOI.get(model, MOI.PrimalStatus()) == MOI.FEASIBLE_POINT
+        @test MOI.get(model, MOI.ObjectiveValue()) ≈ 28.75 atol=atol rtol=rtol
+        @test MOI.get(model, MOI.VariablePrimal(), x1) ≈ 1.25 atol=atol rtol=rtol
+        @test MOI.get(model, MOI.VariablePrimal(), x2) ≈ 8.75 atol=atol rtol=rtol
+        @test MOI.get(model, MOI.VariablePrimal(), z1) ≈ 0.0 atol=atol rtol=rtol
+        @test MOI.get(model, MOI.VariablePrimal(), z2) ≈ 1.0 atol=atol rtol=rtol
+    end
+end
+
+function indicator2_test(model::MOI.ModelLike, config::TestConfig)
+    atol = config.atol
+    rtol = config.rtol
+    # linear problem with indicator constraint
+    # max  2x1 + 3x2 - 30 z2
+    # s.t. x1 + x2 <= 10
+    #      z1 ==> x2 <= 8
+    #      z2 ==> x2 + x1/5 <= 9
+    #      z1 + z2 >= 1
+
+    MOI.empty!(model)
+    @test MOI.is_empty(model)
+
+    # This is the same model as indicator_test1, except that the penalty on z2 forces z1 to be 1.
+
+    x1 = MOI.add_variable(model)
+    x2 = MOI.add_variable(model)
+    z1  = MOI.add_variable(model)
+    z2  = MOI.add_variable(model)
+    MOI.add_constraint(model, z1, MOI.ZeroOne())
+    MOI.add_constraint(model, z2, MOI.ZeroOne())
+    f1 = MOI.VectorAffineFunction(
+        [MOI.VectorAffineTerm(1, MOI.ScalarAffineTerm(1.0, z1)),
+         MOI.VectorAffineTerm(2, MOI.ScalarAffineTerm(1.0, x2)),
+        ],
+        [0.0, 0.0]
+    )
+    iset1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(8.0))
+    MOI.add_constraint(model, f1, iset1)
+
+    f2 = MOI.VectorAffineFunction(
+        [MOI.VectorAffineTerm(1, MOI.ScalarAffineTerm(1.0, z2)),
+         MOI.VectorAffineTerm(2, MOI.ScalarAffineTerm(0.2, x1)),
+         MOI.VectorAffineTerm(2, MOI.ScalarAffineTerm(1.0, x2)),
+        ],
+        [0.0, 0.0],
+    )
+    iset2 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
+
+    MOI.add_constraint(model, f2, iset2)
+
+    # additional regular constraint
+    MOI.add_constraint(model,
+        MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(1.0, x1), MOI.ScalarAffineTerm(1.0, x2)], 0.0),
+        MOI.LessThan(10.0),
+    )
+
+    # disjunction z1 ⋁ z2
+    MOI.add_constraint(model,
+        MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(1.0, z1), MOI.ScalarAffineTerm(1.0, z2)], 0.0),
+        MOI.GreaterThan(1.0),
+    )
+
+    # objective penalized on z2
+    MOI.set(model, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}(),
+        MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([2.0, 3.0, -30.0], [x1, x2, z2]), 0.0)
+    )
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
+
+    if config.solve
+        @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
+
+        MOI.optimize!(model)
+
+        @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMAL
+        @test MOI.get(model, MOI.PrimalStatus()) == MOI.FEASIBLE_POINT
+        @test MOI.get(model, MOI.ObjectiveValue()) ≈ 28.0 atol=atol rtol=rtol
+        @test MOI.get(model, MOI.VariablePrimal(), x1) ≈ 2.0  atol=atol rtol=rtol
+        @test MOI.get(model, MOI.VariablePrimal(), x2) ≈ 8.0  atol=atol rtol=rtol
+        @test MOI.get(model, MOI.VariablePrimal(), z1) ≈ 1.0 atol=atol rtol=rtol
+        @test MOI.get(model, MOI.VariablePrimal(), z2) ≈ 0.0 atol=atol rtol=rtol
+    end
+end
+
+function indicator3_test(model::MOI.ModelLike, config::TestConfig)
+    atol = config.atol
+    rtol = config.rtol
+    # linear problem with indicator constraint
+    # similar to indicator1_test with reversed z1
+    # max  2x1 + 3x2
+    # s.t. x1 + x2 <= 10
+    #      z1 == 0 ==> x2 <= 8
+    #      z2 == 1 ==> x2 + x1/5 <= 9
+    #      (1-z1) + z2 >= 1 <=> z2 - z1 >= 0 
+
+    MOI.empty!(model)
+    @test MOI.is_empty(model)
+
+    @test MOI.supports(model, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}())
+    @test MOI.supports(model, MOI.ObjectiveSense())
+    @test MOI.supports_constraint(model, MOI.SingleVariable, MOI.ZeroOne)
+    @test MOI.supports_constraint(model, MOI.SingleVariable, MOI.Interval{Float64})
+    @test MOI.supports_constraint(model, MOI.ScalarAffineFunction{Float64}, MOI.Interval{Float64})
+    @test MOI.supports_constraint(model, MOI.VectorAffineFunction{Float64}, MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE, MOI.LessThan{Float64}})
+    x1 = MOI.add_variable(model)
+    x2 = MOI.add_variable(model)
+    z1 = MOI.add_variable(model)
+    z2 = MOI.add_variable(model)
+    MOI.add_constraint(model, z1, MOI.ZeroOne())
+    MOI.add_constraint(model, z2, MOI.ZeroOne())
+    f1 = MOI.VectorAffineFunction(
+        [MOI.VectorAffineTerm(1, MOI.ScalarAffineTerm(1.0, z1)),
+         MOI.VectorAffineTerm(2, MOI.ScalarAffineTerm(1.0, x2)),
+        ],
+        [0.0, 0.0]
+    )
+    iset1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO}(MOI.LessThan(8.0))
+    MOI.add_constraint(model, f1, iset1)
+
+    f2 = MOI.VectorAffineFunction(
+        [MOI.VectorAffineTerm(1, MOI.ScalarAffineTerm(1.0, z2)),
+         MOI.VectorAffineTerm(2, MOI.ScalarAffineTerm(0.2, x1)),
+         MOI.VectorAffineTerm(2, MOI.ScalarAffineTerm(1.0, x2)),
+        ],
+        [0.0, 0.0],
+    )
+    iset2 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
+
+    MOI.add_constraint(model, f2, iset2)
+
+    # Additional regular constraint.
+    MOI.add_constraint(model,
+        MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(1.0, x1), MOI.ScalarAffineTerm(1.0, x2)], 0.0),
+        MOI.LessThan(10.0),
+    )
+
+    # Disjunction (1-z1) ⋁ z2
+    MOI.add_constraint(model,
+        MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(-1.0, z1), MOI.ScalarAffineTerm(1.0, z2)], 0.0),
+        MOI.GreaterThan(0.0),
+    )
+
+    MOI.set(model, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}(),
+        MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([2.0, 3.0], [x1, x2]), 0.0)
+    )
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
+
+    if config.solve
+        @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
+
+        MOI.optimize!(model)
+
+        @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMAL
+        @test MOI.get(model, MOI.PrimalStatus()) == MOI.FEASIBLE_POINT
+        @test MOI.get(model, MOI.ObjectiveValue()) ≈ 28.75 atol=atol rtol=rtol
+        @test MOI.get(model, MOI.VariablePrimal(), x1) ≈ 1.25 atol=atol rtol=rtol
+        @test MOI.get(model, MOI.VariablePrimal(), x2) ≈ 8.75 atol=atol rtol=rtol
+        @test MOI.get(model, MOI.VariablePrimal(), z1) ≈ 1.0 atol=atol rtol=rtol
+        @test MOI.get(model, MOI.VariablePrimal(), z2) ≈ 1.0 atol=atol rtol=rtol
+    end
+end
+
 const intlineartests = Dict("knapsack" => knapsacktest,
                             "int1"     => int1test,
                             "int2"     => int2test,
-                            "int3"     => int3test)
+                            "int3"     => int3test,
+                            "indicator1"  => indicator1_test,
+                            "indicator2"  => indicator2_test,
+                            "indicator3"  => indicator3_test,
+                           )
 
 @moitestset intlinear
diff --git a/src/sets.jl b/src/sets.jl
index 9e12d83b97..4797e8ad69 100644
--- a/src/sets.jl
+++ b/src/sets.jl
@@ -435,6 +435,57 @@ Base.isapprox(a::T, b::T; kwargs...) where {T <: Union{SOS1, SOS2}} = isapprox(a
 
 dimension(s::Union{SOS1, SOS2}) = length(s.weights)
 
+"""
+	ActivationCondition
+
+Activation condition for an indicator constraint.
+The enum value is used as first type parameter of `IndicatorSet{A,S}`.
+"""
+@enum ActivationCondition begin
+    ACTIVATE_ON_ZERO
+    ACTIVATE_ON_ONE
+end
+
+"""
+    IndicatorSet{A, S <: AbstractScalarSet}(set::S)
+
+``\\{((y, x) \\in \\{0, 1\\} \\times \\mathbb{R}^n : y = 0 \\implies x \\in set\\}``
+when `A` is `ACTIVATE_ON_ZERO` and
+``\\{((y, x) \\in \\{0, 1\\} \\times \\mathbb{R}^n : y = 1 \\implies x \\in set\\}``
+when `A` is `ACTIVATE_ON_ONE`.
+
+`S` has to be a sub-type of `AbstractScalarSet`.
+`A` is one of the value of the `ActivationCond` enum.
+`IndicatorSet` is used with a `VectorAffineFunction` holding
+the indicator variable first.
+
+Example: ``\\{(y, x) \\in \\{0, 1\\} \\times \\mathbb{R}^2 : y = 1 \\implies x_1 + x_2 \\leq 9 \\} ``
+
+```julia
+f = MOI.VectorAffineFunction(
+    [MOI.VectorAffineTerm(1, MOI.ScalarAffineTerm(1.0, z)),
+     MOI.VectorAffineTerm(2, MOI.ScalarAffineTerm(0.2, x1)),
+     MOI.VectorAffineTerm(2, MOI.ScalarAffineTerm(1.0, x2)),
+    ],
+    [0.0, 0.0],
+)
+
+indicator_set = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(9.0))
+
+MOI.add_constraint(model, f, indicator_set)
+```
+"""
+struct IndicatorSet{A, S <: AbstractScalarSet} <: AbstractVectorSet
+    set::S
+    IndicatorSet{A}(set::S) where {A, S <: AbstractScalarSet} = new{A,S}(set)
+end
+
+dimension(::IndicatorSet) = 2
+
+function Base.copy(set::IndicatorSet{A,S}) where {A,S}
+    return IndicatorSet{A}(copy(set.set))
+end
+
 # isbits types, nothing to copy
 function Base.copy(set::Union{Reals, Zeros, Nonnegatives, Nonpositives,
                               GreaterThan, LessThan, EqualTo, Interval,
diff --git a/test/Test/intlinear.jl b/test/Test/intlinear.jl
index 0bcbea02b7..000473bc06 100644
--- a/test/Test/intlinear.jl
+++ b/test/Test/intlinear.jl
@@ -28,3 +28,15 @@ MOIT.int3test(mock, config)
 MOIU.set_mock_optimize!(mock,
     (mock::MOIU.MockOptimizer) -> MOIU.mock_optimize!(mock, [1, 0, 0, 1, 1]))
 MOIT.knapsacktest(mock, config)
+MOIU.set_mock_optimize!(mock,
+    (mock::MOIU.MockOptimizer) -> MOIU.mock_optimize!(mock, [1.25, 8.75, 0., 1.])
+)
+MOIT.indicator1_test(mock, config)
+MOIU.set_mock_optimize!(mock,
+    (mock::MOIU.MockOptimizer) -> MOIU.mock_optimize!(mock, [2.0, 8.0, 1., 0.])
+)
+MOIT.indicator2_test(mock, config)
+MOIU.set_mock_optimize!(mock,
+    (mock::MOIU.MockOptimizer) -> MOIU.mock_optimize!(mock, [1.25, 8.75, 1., 1.])
+)
+MOIT.indicator3_test(mock, config)
diff --git a/test/model.jl b/test/model.jl
index 9dc02cfc17..1c1a5b6c77 100644
--- a/test/model.jl
+++ b/test/model.jl
@@ -1,5 +1,10 @@
+
+const LessThanIndicatorSetOne{T} = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE, MOI.LessThan{T}}
+const LessThanIndicatorSetZero{T} = MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO, MOI.LessThan{T}}
+
 # Needed by test spread over several files, defining it here make it easier to comment out tests
 # Model supporting every MOI functions and sets
+
 MOIU.@model(Model,
             (MOI.ZeroOne, MOI.Integer),
             (MOI.EqualTo, MOI.GreaterThan, MOI.LessThan, MOI.Interval,
@@ -10,7 +15,7 @@ MOIU.@model(Model,
              MOI.PositiveSemidefiniteConeTriangle, MOI.PositiveSemidefiniteConeSquare,
              MOI.RootDetConeTriangle, MOI.RootDetConeSquare, MOI.LogDetConeTriangle,
              MOI.LogDetConeSquare),
-            (MOI.PowerCone, MOI.DualPowerCone, MOI.SOS1, MOI.SOS2),
+            (MOI.PowerCone, MOI.DualPowerCone, MOI.SOS1, MOI.SOS2, LessThanIndicatorSetOne, LessThanIndicatorSetZero),
             (MOI.SingleVariable,),
             (MOI.ScalarAffineFunction, MOI.ScalarQuadraticFunction),
             (MOI.VectorOfVariables,),
diff --git a/test/sets.jl b/test/sets.jl
index 6374184a9e..deb82310e8 100644
--- a/test/sets.jl
+++ b/test/sets.jl
@@ -1,3 +1,15 @@
+"""
+    MutLessThan{T<:Real} <: MOI.AbstractScalarSet
+
+A mutable `LessThan`-like set to test `copy` of indicator set
+"""
+mutable struct MutLessThan{T<:Real} <: MOI.AbstractScalarSet
+    upper::T
+    MutLessThan(v::T) where {T<:Real} = new{T}(v)
+end
+
+Base.copy(mlt::MutLessThan) = MutLessThan(Base.copy(mlt.upper))
+
 @testset "Sets" begin
     @testset "Copy" begin
         @testset "for $S" for S in [MOI.SOS1, MOI.SOS2]
@@ -6,5 +18,21 @@
             s_copy.weights[1] = 2.0
             @test s.weights[1] == 1.0
         end
+        @testset "IndicatorSet" begin
+            s1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(4.0))
+            s2 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO}(MOI.GreaterThan(4.0))
+            s1_copy = copy(s1)
+            s2_copy = copy(s2)
+            @test s1_copy isa MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}
+            @test s1 == s1_copy
+            @test s2_copy isa MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO}
+            @test s2 == s2_copy
+            s3 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ZERO}(MutLessThan(4.0))
+            s3_copy = copy(s3)
+            @test s3.set.upper ≈ 4.0
+            s3_copy.set.upper = 5.0
+            @test s3.set.upper ≈ 4.0
+            @test s3_copy.set.upper ≈ 5.0    
+        end
     end
 end