diff --git a/src/Utilities/functions.jl b/src/Utilities/functions.jl
index 80d618b741..e384587147 100644
--- a/src/Utilities/functions.jl
+++ b/src/Utilities/functions.jl
@@ -92,6 +92,8 @@ function value_type(
     return MA.promote_operation(*, C, T)
 end
 
+value_type(::Type{T}, ::Type{MOI.ScalarNonlinearFunction}) where {T} = T
+
 function value_type(
     ::Type{T},
     ::Type{F},
@@ -325,6 +327,7 @@ function map_indices(
     index_map::F,
     f::MOI.ScalarNonlinearFunction,
 ) where {F<:Function}
+    # TODO(odow): this uses recursion. We should remove at some point.
     return MOI.ScalarNonlinearFunction(
         f.head,
         convert(Vector{Any}, map_indices(index_map, f.args)),
@@ -466,6 +469,17 @@ function substitute_variables(
     return g
 end
 
+function substitute_variables(
+    variable_map::F,
+    f::MOI.ScalarNonlinearFunction,
+) where {F<:Function}
+    # TODO(odow): this uses recursion. We should remove at some point.
+    return MOI.ScalarNonlinearFunction(
+        f.head,
+        Any[substitute_variables(variable_map, a) for a in f.args],
+    )
+end
+
 function substitute_variables(
     variable_map::F,
     f::MOI.VectorAffineFunction{T},
@@ -823,10 +837,32 @@ function unsafe_add(
     return T(t1.output_index, scalar_term)
 end
 
+# Generic fallback for items inside NonlinearFunctions like numbers.
+is_canonical(::Any) = true
+
 is_canonical(::MOI.AbstractFunction) = false
 
 is_canonical(::Union{MOI.VariableIndex,MOI.VectorOfVariables}) = true
 
+function is_canonical(f::MOI.ScalarNonlinearFunction)
+    # Don't use recursion here! This gets called for all scalar nonlinear
+    # constraints.
+    stack = Any[arg for arg in f.args]
+    while !isempty(stack)
+        arg = pop!(stack)
+        if arg isa MOI.ScalarNonlinearFunction
+            for a in arg.args
+                push!(stack, a)
+            end
+        else
+            if !is_canonical(arg)
+                return false
+            end
+        end
+    end
+    return true
+end
+
 """
     is_canonical(f::Union{ScalarAffineFunction, VectorAffineFunction})
 
@@ -919,7 +955,14 @@ function canonicalize!(
     return f
 end
 
-canonicalize!(f::MOI.ScalarNonlinearFunction) = f
+function canonicalize!(f::MOI.ScalarNonlinearFunction)
+    for (i, arg) in enumerate(f.args)
+        if !is_canonical(arg)
+            f.args[i] = canonicalize!(arg)
+        end
+    end
+    return f
+end
 
 """
     canonicalize!(f::Union{ScalarQuadraticFunction, VectorQuadraticFunction})
diff --git a/test/Utilities/functions.jl b/test/Utilities/functions.jl
index 79b214f5fc..3374c04b46 100644
--- a/test/Utilities/functions.jl
+++ b/test/Utilities/functions.jl
@@ -1844,6 +1844,7 @@ function test_value_type()
         T,
         MOI.ScalarQuadraticFunction{Complex{Int}},
     ) == Complex{T}
+    @test MOI.Utilities.value_type(T, MOI.ScalarNonlinearFunction) == T
     @test MOI.Utilities.value_type(
         T,
         MOI.ScalarQuadraticFunction{Complex{T}},
@@ -1909,6 +1910,45 @@ function test_ScalarNonlinearFunction_count_map_indices_and_print()
     return
 end
 
+function test_ScalarNonlinearFunction_map_indices()
+    src = MOI.Utilities.Model{Float64}()
+    x = MOI.add_variable(src)
+    f = MOI.ScalarNonlinearFunction(:log, Any[x])
+    c = MOI.add_constraint(src, f, MOI.LessThan(1.0))
+    dest = MOI.Utilities.Model{Float64}()
+    index_map = MOI.copy_to(dest, src)
+    new_f = MOI.Utilities.map_indices(index_map, f)
+    @test new_f ≈ MOI.ScalarNonlinearFunction(:log, Any[index_map[x]])
+    return
+end
+
+function test_ScalarNonlinearFunction_substitute_variables()
+    x = MOI.VariableIndex(1)
+    f = MOI.ScalarNonlinearFunction(:log, Any[1.0*x])
+    new_f = MOI.Utilities.substitute_variables(x -> -2.0 * x, f)
+    @test new_f ≈ MOI.ScalarNonlinearFunction(:log, Any[-2.0*x])
+    return
+end
+
+function test_ScalarNonlinearFunction_is_canonical()
+    x = MOI.VariableIndex(1)
+    f = MOI.ScalarNonlinearFunction(:log, Any[1.0*x])
+    @test MOI.Utilities.is_canonical(f)
+    g = MOI.ScalarNonlinearFunction(:log, Any[1.0*x+1.0*x])
+    @test !MOI.Utilities.is_canonical(g)
+    MOI.Utilities.canonicalize!(g)
+    @test MOI.Utilities.is_canonical(g)
+    @test g.args[1] ≈ 2.0 * x
+    f = MOI.ScalarNonlinearFunction(:^, Any[x, 2])
+    @test MOI.Utilities.is_canonical(f)
+    # Test deep recursion
+    for _ in 1:100_000
+        f = MOI.ScalarNonlinearFunction(:sin, Any[f])
+    end
+    @test MOI.Utilities.is_canonical(f)
+    return
+end
+
 function test_vector_type()
     for T in (Int, Float64)
         @test MOI.Utilities.vector_type(T) == Vector{T}