diff --git a/Project.toml b/Project.toml
index 2e38c8e..84755d8 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,23 +1,15 @@
 name = "MLJIteration"
 uuid = "614be32b-d00c-4edb-bd02-1eb411ab5e55"
 authors = ["Anthony D. Blaom <anthony.blaom@gmail.com>"]
-version = "0.4.5"
+version = "0.5.0"
 
 [deps]
 IterationControl = "b3c1a2ee-3fec-4384-bf48-272ea71de57c"
 MLJBase = "a7f614a8-145f-11e9-1d2a-a57a1082229d"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+Serialization = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 
 [compat]
+MLJBase = "0.20"
 IterationControl = "0.5"
-MLJBase = "0.18.8, 0.19"
 julia = "1.6"
-
-[extras]
-MLJModelInterface = "e80e1ace-859a-464e-9ed9-23947d8ae3ea"
-StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
-Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
-Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-
-[targets]
-test = ["MLJModelInterface", "StableRNGs", "Statistics", "Test"]
diff --git a/src/MLJIteration.jl b/src/MLJIteration.jl
index b390817..dfe9cd7 100644
--- a/src/MLJIteration.jl
+++ b/src/MLJIteration.jl
@@ -1,5 +1,6 @@
 module MLJIteration
 
+using Serialization
 using MLJBase
 using IterationControl
 import IterationControl: debug, skip, composite
@@ -14,7 +15,8 @@ const CONTROLS = vcat(IterationControl.CONTROLS,
                        :WithReportDo,
                        :WithMachineDo,
                        :WithModelDo,
-                       :CycleLearningRate])
+                       :CycleLearningRate,
+                       :Save])
 
 const TRAINING_CONTROLS = [:Step, ]
 
diff --git a/src/controls.jl b/src/controls.jl
index 8b72755..38e8dee 100644
--- a/src/controls.jl
+++ b/src/controls.jl
@@ -167,3 +167,41 @@ function IterationControl.update!(control::CycleLearningRate,
 end
 
 
+# # SAVE CONTROL
+struct Save{F<:Function}
+    filename::String
+    method::F
+end
+
+Save(filename; method=serialize) =
+    Save(filename, method)
+
+Save(;filename="machine.jls", method=serialize) = 
+    Save(filename, method)
+
+IterationControl.@create_docs(Save,
+             header="Save(filename=\"machine.jls\")",
+             example="Save(\"run3/machine.jls\")",
+             body="Save the current state of the machine being iterated to "*
+             "disk, using the provided `filename`, decorated with a number, "*
+             "as in \"run3/machine42.jls\". The default behaviour uses "*
+             "the Serialization module but this can be changed by setting "*
+             "the `method=save_fn(::String, ::Any)` argument where `save_fn` "*
+             "is any serialization method. "*
+             "For more on what is meant by \"the machine being iterated\", "*
+             "see [`IteratedModel`](@ref).")
+
+function IterationControl.update!(c::Save,
+                                  ic_model,
+                                  verbosity,
+                                  n,
+                                  state=(filenumber=0, ))
+    filenumber = state.filenumber + 1
+    root, suffix = splitext(c.filename)
+    filename = string(root, filenumber, suffix)
+    train_mach = IterationControl.expose(ic_model)
+    verbosity > 0 && @info "Saving \"$filename\". "
+    strain_mach = MLJBase.serializable(train_mach)
+    c.method(filename, strain_mach)
+    return (filenumber=filenumber, )
+end
diff --git a/test/Project.toml b/test/Project.toml
new file mode 100644
index 0000000..eec0b36
--- /dev/null
+++ b/test/Project.toml
@@ -0,0 +1,14 @@
+[deps]
+IterationControl = "b3c1a2ee-3fec-4384-bf48-272ea71de57c"
+JLSO = "9da8a3cd-07a3-59c0-a743-3fdc52c30d11"
+MLJBase = "a7f614a8-145f-11e9-1d2a-a57a1082229d"
+MLJModelInterface = "e80e1ace-859a-464e-9ed9-23947d8ae3ea"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+Serialization = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
+StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[compat]
+MLJModelInterface = "1.3"
+StableRNGs = "1.0"
diff --git a/test/controls.jl b/test/controls.jl
index 1beb432..0bed8fb 100644
--- a/test/controls.jl
+++ b/test/controls.jl
@@ -4,7 +4,10 @@ using MLJIteration
 using MLJBase
 using Test
 using ..DummyModel
+using JLSO
+using Serialization
 using IterationControl
+
 const IC = IterationControl
 
 const X, y = make_dummy(N=8);
@@ -189,5 +192,46 @@ end
     @test model.learning_rate == 0.5
 end
 
+
+jlso_save(filename, mach) = JLSO.save(filename, :machine => mach)
+function jlso_machine(filename)
+    mach = JLSO.load(filename)[:machine]
+    MLJBase.restore!(mach)
+    return mach
+end
+
+@testset "Save" begin
+    # Test constructors
+    filename = "serialization_test.jls"
+    c_ = Save(filename)
+    c = Save(filename=filename)
+    @test c == c_
+    # Test control for Serialization `serialize` and JLSO `save`
+    for (save_fn,load_fn) in (serialize => MLJBase.machine, jlso_save => jlso_machine)
+        c = Save(filename, method=save_fn)
+        m = machine(DummyIterativeModel(n=2), X, y)
+        fit!(m, verbosity=0)
+        state = @test_logs((:info, "Saving \"serialization_test1.jls\". "),
+        IterationControl.update!(c, m, 2, 1))
+        @test state.filenumber == 1
+        m.model.n = 5
+        fit!(m, verbosity=0)
+        state = IterationControl.update!(c, m, 0, 2, state)
+        @test state.filenumber == 2
+        yhat = predict(IterationControl.expose(m), X);
+
+        deserialized_mach = load_fn("serialization_test2.jls")
+        yhat2 = predict(deserialized_mach, X)
+        @test yhat2 ≈ yhat
+
+        train_mach = machine(DummyIterativeModel(n=5), X, y)
+        fit!(train_mach, verbosity=0)
+        @test yhat ≈ predict(train_mach, X)
+
+        rm("serialization_test1.jls")
+        rm("serialization_test2.jls")
+    end
+end
+
 end
 true