diff --git a/README.md b/README.md
index 3315820..fe9349c 100644
--- a/README.md
+++ b/README.md
@@ -54,7 +54,7 @@ system, `$SCIPOPTDIR/lib/libscip.so`, `$SCIPOPTDIR/lib/libscip.dylib`, or
 `$SCIPOPTDIR/bin/libscip.dll` must exist). Then, install `SCIP.jl` using `Pkg.add`
 and `Pkg.build` from the Julia command line:
 ```julia
-julia> ENV["SCIPOPTDIR"] = raw"C:\Program Files\SCIPOptSuite 9.1.1" # for Windows
+julia> ENV["SCIPOPTDIR"] = raw"C:\Program Files\SCIPOptSuite 10.0.0" # for Windows
 
 julia> import Pkg
 
diff --git a/src/MOI_wrapper/conflict.jl b/src/MOI_wrapper/conflict.jl
index c91e03c..ec641af 100644
--- a/src/MOI_wrapper/conflict.jl
+++ b/src/MOI_wrapper/conflict.jl
@@ -143,3 +143,163 @@ function MOI.get(
     slack_value = SCIPgetSolVal(o, sol, ptr)
     return slack_value > 0.5 ? MOI.IN_CONFLICT : MOI.NOT_IN_CONFLICT
 end
+
+## IIS & MOI conflicts
+
+function has_all_names(o::Optimizer)
+    for vidx in MOI.get(o, MOI.ListOfVariableIndices())
+        if MOI.get(o, MOI.VariableName(), vidx) == ""
+            return false
+        end
+    end
+    for (F, S) in MOI.get(o, MOI.ListOfConstraintTypesPresent())
+        if F === MOI.VariableIndex
+            continue
+        end
+        for cidx in MOI.get(o, MOI.ListOfConstraintIndices{F,S}())
+            if MOI.get(o, MOI.ConstraintName(), cidx) === nothing ||
+               MOI.get(o, MOI.ConstraintName(), cidx) == ""
+                return false
+            end
+        end
+    end
+    return true
+end
+
+function set_default_names!(o::Optimizer)
+    for vidx in MOI.get(o, MOI.ListOfVariableIndices())
+        if MOI.get(o, MOI.VariableName(), vidx) == ""
+            MOI.set(o, MOI.VariableName(), vidx, "x$(vidx.value)")
+        end
+    end
+    for (F, S) in MOI.get(o, MOI.ListOfConstraintTypesPresent())
+        if F === MOI.VariableIndex
+            continue
+        end
+        for cidx in MOI.get(o, MOI.ListOfConstraintIndices{F,S}())
+            if MOI.get(o, MOI.ConstraintName(), cidx) === nothing ||
+               MOI.get(o, MOI.ConstraintName(), cidx) == ""
+                MOI.set(o, MOI.ConstraintName(), cidx, "$(string(cidx))")
+            end
+        end
+    end
+    return
+end
+
+function MOI.compute_conflict!(o::Optimizer)
+    if !has_all_names(o::Optimizer)
+        error(
+            "SCIP requires all variables and constraints to have a name set for the IIS to work.",
+        )
+    end
+    @SCIP_CALL SCIP.LibSCIP.SCIPgenerateIIS(o)
+    return
+end
+
+function MOI.get(o::Optimizer, ::MOI.ConflictStatus)
+    iis = SCIP.LibSCIP.SCIPgetIIS(o)
+    is_infeasible = SCIP.LibSCIP.SCIPiisIsSubscipInfeasible(iis)
+    st = MOI.get(o, MOI.TerminationStatus())
+    # we ignore MOI.NO_CONFLICT_FOUND for now
+    # this is not supposed to happen with a greedy method
+    if st != MOI.INFEASIBLE
+        return MOI.NO_CONFLICT_EXISTS
+    elseif is_infeasible == 0
+        return MOI.COMPUTE_CONFLICT_NOT_CALLED
+    else
+        return MOI.CONFLICT_FOUND
+    end
+end
+
+function MOI.get(
+    o::Optimizer,
+    ::MOI.ConstraintConflictStatus,
+    index::MOI.ConstraintIndex{MOI.VariableIndex,S},
+) where {S<:Union{MOI.LessThan,MOI.EqualTo,MOI.GreaterThan}}
+    if MOI.get(o, MOI.ConflictStatus()) != MOI.CONFLICT_FOUND
+        return MOI.NOT_IN_CONFLICT
+    end
+    set = MOI.get(o, MOI.ConstraintSet(), index)
+    bound_values = bounds(o, set)
+    index_var_name =
+        MOI.get(o, MOI.VariableName(), MOI.VariableIndex(index.value))
+    nvars = SCIP.LibSCIP.SCIPgetNOrigVars(iis_subscip)
+    vars_ptr = SCIP.LibSCIP.SCIPgetOrigVars(iis_subscip)
+    raw_vars_vec = unsafe_wrap(Array, vars_ptr, nvars)
+    for var in raw_vars_vec
+        var_name = unsafe_string(SCIP.LibSCIP.SCIPvarGetName(var))
+        if var_name == index_var_name
+            lb = SCIP.LibSCIP.SCIPvarGetUbOriginal(var)
+            ub = SCIP.LibSCIP.SCIPvarGetUbOriginal(var)
+            if bound_values[1] ≈ lb && bound_values[2] ≈ ub
+                return MOI.IN_CONFLICT
+            end
+            return MOI.NOT_IN_CONFLICT
+        end
+    end
+    # variable not present in the IIS subproblem
+    return MOI.NOT_IN_CONFLICT
+end
+
+function MOI.get(
+    o::Optimizer,
+    ::MOI.ConstraintConflictStatus,
+    index::MOI.ConstraintIndex{F,S},
+) where {
+    F<:Union{
+        MOI.ScalarAffineFunction,
+        MOI.VectorOfVariables,
+        MOI.ScalarQuadraticFunction,
+    },
+    S,
+}
+    if MOI.get(o, MOI.ConflictStatus()) != MOI.CONFLICT_FOUND
+        return MOI.NOT_IN_CONFLICT
+    end
+    c_name = MOI.get(o, MOI.ConstraintName(), index)
+    iis_subscip = SCIP.LibSCIP.SCIPiisGetSubscip(SCIP.LibSCIP.SCIPgetIIS(o))
+    n_cons = SCIP.LibSCIP.SCIPgetNOrigConss(iis_subscip)
+    cons_ptr = SCIP.LibSCIP.SCIPgetOrigConss(iis_subscip)
+    raw_cons_vec = unsafe_wrap(Array, cons_ptr, n_cons)
+    for cons in raw_cons_vec
+        cons_name = unsafe_string(SCIP.LibSCIP.SCIPconsGetName(cons))
+        if cons_name == c_name
+            return MOI.IN_CONFLICT
+        end
+    end
+    return MOI.NOT_IN_CONFLICT
+end
+
+function MOI.get(
+    o::Optimizer,
+    ::MOI.ConstraintConflictStatus,
+    index::MOI.ConstraintIndex{
+        MOI.VariableIndex,
+        <:Union{MOI.Integer,MOI.ZeroOne},
+    },
+)
+    if MOI.get(o, MOI.ConflictStatus()) != MOI.CONFLICT_FOUND
+        return MOI.NOT_IN_CONFLICT
+    end
+    if !MOI.is_valid(model, index)
+        throw(MOI.InvalidIndex(index))
+    end
+    index_var_name =
+        MOI.get(o, MOI.VariableName(), MOI.VariableIndex(index.value))
+    nvars = SCIP.LibSCIP.SCIPgetNOrigVars(iis_subscip)
+    vars_ptr = SCIP.LibSCIP.SCIPgetOrigVars(iis_subscip)
+    raw_vars_vec = unsafe_wrap(Array, vars_ptr, nvars)
+    for var in raw_vars_vec
+        var_name = unsafe_string(SCIP.LibSCIP.SCIPvarGetName(var))
+        if var_name == index_var_name
+            if SCIP.LibSCIP.SCIPvarIsBinary(var) ||
+               SCIP.LibSCIP.SCIPvarIsIntegral(var)
+                # we cannot ensure the integrality constraint is in the conflict
+                return MOI.MAYBE_IN_CONFLICT
+            end
+            return MOI.NOT_IN_CONFLICT
+        end
+    end
+
+    return MOI.MAYBE_IN_CONFLICT
+end
diff --git a/test/MOI_tests.jl b/test/MOI_tests.jl
index 79c28c7..7922926 100644
--- a/test/MOI_tests.jl
+++ b/test/MOI_tests.jl
@@ -1692,6 +1692,55 @@ function test_fix_binary_variable()
     return
 end
 
+function test_SOS1_no_conflict()
+    model = SCIP.Optimizer()
+    MOI.set(model, MOI.Silent(), true)
+    x = MOI.add_variables(model, 2)
+    set = MOI.SOS1([1.0, 2.0])
+    c1 = MOI.add_constraint(model, MOI.VectorOfVariables(x), set)
+    SCIP.set_default_names!(model)
+    MOI.optimize!(model)
+    MOI.compute_conflict!(model)
+    @test MOI.get(model, MOI.ConstraintConflictStatus(), c1) ==
+          MOI.NOT_IN_CONFLICT
+    return
+end
+
+function test_SOS1_in_conflict()
+    model = SCIP.Optimizer()
+    MOI.set(model, MOI.Silent(), true)
+    x = MOI.add_variables(model, 2)
+    MOI.add_constraint.(model, x, MOI.GreaterThan(0.0))
+    MOI.add_constraint.(model, x, MOI.LessThan(1.0))
+    set = MOI.SOS1([1.0, 2.0])
+    c1 = MOI.add_constraint(model, MOI.VectorOfVariables(x), set)
+    c2 = MOI.add_constraint(model, 1.0 * x[1] + 1.0 * x[2], MOI.EqualTo(2.0))
+    SCIP.set_default_names!(model)
+    MOI.optimize!(model)
+    MOI.compute_conflict!(model)
+    @test MOI.get(model, MOI.ConstraintConflictStatus(), c1) == MOI.IN_CONFLICT
+    @test MOI.get(model, MOI.ConstraintConflictStatus(), c2) == MOI.IN_CONFLICT
+    return
+end
+
+function test_SOS2_not_in_conflict()
+    model = SCIP.Optimizer()
+    MOI.set(model, MOI.Silent(), true)
+    x = MOI.add_variables(model, 3)
+    MOI.add_constraint.(model, x, MOI.GreaterThan(0.0))
+    set = MOI.SOS2([1.0, 2.0, 3.0])
+    c1 = MOI.add_constraint(model, MOI.VectorOfVariables(x), set)
+    f = sum(1.0 * x[i] for i in 1:3)
+    c2 = MOI.add_constraint(model, f, MOI.EqualTo(-1.0))
+    SCIP.set_default_names!(model)
+    MOI.optimize!(model)
+    MOI.compute_conflict!(model)
+    @test MOI.get(model, MOI.ConstraintConflictStatus(), c1) ==
+          MOI.NOT_IN_CONFLICT
+    @test MOI.get(model, MOI.ConstraintConflictStatus(), c2) == MOI.IN_CONFLICT
+    return
+end
+
 end  # module TestMOIWrapper
 
 TestMOIWrapper.runtests()
diff --git a/test/iis.jl b/test/iis.jl
new file mode 100644
index 0000000..dd9803e
--- /dev/null
+++ b/test/iis.jl
@@ -0,0 +1,53 @@
+using SCIP
+using Test
+import MathOptInterface as MOI
+
+@testset "Basic conflict with raw SCIP API" begin
+    o = SCIP.Optimizer()
+
+    x, _ = MOI.add_constrained_variable(o, MOI.ZeroOne())
+    y, _ = MOI.add_constrained_variable(o, MOI.ZeroOne())
+    z, _ = MOI.add_constrained_variable(o, MOI.ZeroOne())
+    w, _ = MOI.add_constrained_variable(o, MOI.ZeroOne())
+
+    MOI.set(o, MOI.VariableName(), x, "x")
+    MOI.set(o, MOI.VariableName(), y, "y")
+    MOI.set(o, MOI.VariableName(), z, "z")
+    MOI.set(o, MOI.VariableName(), w, "w")
+
+    MOI.add_constraint(o, 1.0x + y, MOI.LessThan(1.5))
+    MOI.add_constraint(o, 1.0z + 1.2y, MOI.LessThan(1.3))
+    MOI.add_constraint(o, 1.0z + 1.2y, MOI.LessThan(1.3))
+    MOI.add_constraint(o, 1.0w + 1.2x, MOI.LessThan(1.1))
+
+    MOI.add_constraint(o, 1.0z + 0.9x + 1.2y, MOI.GreaterThan(2.0))
+
+    for S in (MOI.LessThan{Float64}, MOI.GreaterThan{Float64})
+        for cidx in MOI.get(
+            o,
+            MOI.ListOfConstraintIndices{MOI.ScalarAffineFunction{Float64},S}(),
+        )
+            MOI.set(
+                o,
+                MOI.ConstraintName(),
+                cidx,
+                "c$(cidx.value)_$(length(string(S)))",
+            )
+        end
+    end
+
+    @test SCIP.has_all_names(o)
+
+    f_obj = 1.0 * x
+    MOI.set(o, MOI.ObjectiveFunction{typeof(f_obj)}(), f_obj)
+    MOI.set(o, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+
+    MOI.optimize!(o)
+    @test MOI.get(o, MOI.TerminationStatus()) == MOI.INFEASIBLE
+
+    iis = SCIP.LibSCIP.SCIPgetIIS(o)
+    @test SCIP.LibSCIP.SCIPiisIsSubscipInfeasible(iis) == 0
+    SCIP.LibSCIP.SCIPgenerateIIS(o)
+    @test SCIP.LibSCIP.SCIPiisIsSubscipInfeasible(iis) == 1
+    @test SCIP.LibSCIP.SCIPiisIsSubscipIrreducible(iis) == 1
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 1506409..ed04c70 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -21,6 +21,7 @@ include("sepa_support.jl")
 
 @testset "SCIP" begin
     @testset "$file" for file in [
+        "iis.jl",
         "conshdlr.jl",
         "cutsel.jl",
         "direct_library_calls.jl",