diff --git a/Project.toml b/Project.toml
index e20af54..7082957 100644
--- a/Project.toml
+++ b/Project.toml
@@ -4,6 +4,7 @@ authors = ["Michel Schanen <Michel.Schanen@gmail.com>"]
 version = "0.1.0"
 
 [deps]
+Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
 FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 Krylov = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7"
diff --git a/README.md b/README.md
index 8150225..7abeea9 100644
--- a/README.md
+++ b/README.md
@@ -1,7 +1,42 @@
 # DiffKrylov
 [![][build-latest-img]][build-url] [![][codecov-latest-img]][codecov-latest-url]
 
-DiffKrylov provides a differentiable API for [Krylov.jl](https://github.com/JuliaSmoothOptimizers/Krylov.jl) using [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl). In the future, we will also support Enzyme and its reverse mode.
+DiffKrylov provides a differentiable API for
+[Krylov.jl](https://github.com/JuliaSmoothOptimizers/Krylov.jl) using
+[ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl) and
+[Enzyme.jl](https://github.com/EnzymeAD/Enzyme.jl). This is a work in progress and
+eventually should enable numerical comparisons between discrete and continuous
+tangent and adjoint methods (see this
+[report](http://137.226.34.227/Publications/AIB/2012/2012-10.pdf)).
+
+## Current Technical Limitations
+
+* Only supports `gmres`, `cg`, and `bicgstab` methods
+* No support for inplace methods `gmres!`, `cg!`, and `bicgstab!`
+* No support for options when using Enzyme
+* No support for sparse matrices using Enzyme
+* No support for linear operators
+
+## Current Open Questions
+* How to handle preconditioners?
+* How to set the options for the tangent/adjoint solve based on the options for the forward solve? For example `bicgtab` may return `NaN` for the tangents or adjoints.
+
+## Installation
+
+```julia
+] add DiffKrylov
+```
+
+## Usage
+
+Using ForwardDiff.jl, we can compute the Jacobian of `x` with respect to `b` using the ForwardDiff.jl API:
+
+```julia
+using ForwardDiff, DiffKrylov, Krylov, Random
+A = rand(64,64)
+b = rand(64)
+J = ForwardDiff.jacobian(x -> gmres(A, x)[1], b)
+```
 
 [codecov-latest-img]: https://codecov.io/gh/JuliaSmoothOptimizers/DiffKrylov.jl/branch/main/graphs/badge.svg?branch=main
 [codecov-latest-url]: https://codecov.io/github/JuliaSmoothOptimizers/DiffKrylov.jl?branch=main
diff --git a/src/DiffKrylov.jl b/src/DiffKrylov.jl
index ee69a4f..bef9a09 100644
--- a/src/DiffKrylov.jl
+++ b/src/DiffKrylov.jl
@@ -2,5 +2,6 @@ module DiffKrylov
 
 using Krylov
 using SparseArrays
-include("ForwardDiff/krylov.jl")
-end
\ No newline at end of file
+include("ForwardDiff/forwarddiff.jl")
+include("EnzymeRules/enzymerules.jl")
+end
diff --git a/src/EnzymeRules/enzymerules.jl b/src/EnzymeRules/enzymerules.jl
new file mode 100644
index 0000000..fe151ab
--- /dev/null
+++ b/src/EnzymeRules/enzymerules.jl
@@ -0,0 +1,82 @@
+using Enzyme
+import .EnzymeRules: forward, reverse, augmented_primal
+using .EnzymeRules
+
+for solver in (:cg, :bicgstab, :gmres)
+    @eval begin
+        function forward(
+                func::Const{typeof(Krylov.$solver)},
+                RT::Type{<:Union{Const, DuplicatedNoNeed, Duplicated}},
+                _A::Union{Const, Duplicated},
+                _b::Union{Const, Duplicated};
+                options...
+            )
+            A = _A.val
+            b = _b.val
+            dx = []
+            x, stats = Krylov.$solver(A,b; options...)
+            if isa(_A, Duplicated) && isa(_b, Duplicated)
+                dA = _A.dval
+                db = _b.dval
+                db -= dA*x
+                dx, dstats = Krylov.$solver(A,db; options...)
+            elseif isa(_A, Duplicated) && isa(_b, Const)
+                dA = _A.dval
+                db = -dA*x
+                dx, dstats = Krylov.$solver(A,db; options...)
+            elseif isa(_A, Const) && isa(_b, Duplicated)
+                db = _b.dval
+                dx, dstats = Krylov.$solver(A,db; options...)
+            elseif isa(_A, Const) && isa(_b, Const)
+                nothing
+            else
+                error("Error in Krylov forward rule: $(typeof(_A)), $(typeof(_b))")
+            end
+
+            if RT <: Const
+                return (x, stats)
+            elseif RT <: DuplicatedNoNeed
+                return (dx, stats)
+            else
+                return Duplicated((x, stats), (dx, dstats))
+            end
+        end
+    end
+end
+
+export forward
+
+function augmented_primal(
+    config,
+    func::Const{typeof(Krylov.gmres)},
+    ret::Type{<:Duplicated},
+    _A::Union{Const, Duplicated},
+    _b::Union{Const, Duplicated}
+)
+    A = _A.val
+    b = _b.val
+    x, stats = Krylov.gmres(A,b)
+    bx = zeros(length(x))
+    bstats = deepcopy(stats)
+    if needs_primal(config)
+        return AugmentedReturn((x, stats), (bx, bstats), (A,x, Ref(bx)))
+    else
+        return AugmentedReturn(nothing, (bx, bstats), (A,x))
+    end
+end
+
+function reverse(
+    config,
+    ::Const{typeof(Krylov.gmres)},
+    dret,
+    tape,
+    _A,
+    _b
+)
+    (A,x,bx) = tape
+    _b.dval .= gmres(transpose(A), bx[])[1]
+    _A.dval .= -x .* _b.dval'
+    return (nothing, nothing)
+end
+
+export augmented_primal, reverse
diff --git a/src/ForwardDiff/krylov.jl b/src/ForwardDiff/forwarddiff.jl
similarity index 100%
rename from src/ForwardDiff/krylov.jl
rename to src/ForwardDiff/forwarddiff.jl
diff --git a/test/enzymediff.jl b/test/enzymediff.jl
new file mode 100644
index 0000000..be91bb8
--- /dev/null
+++ b/test/enzymediff.jl
@@ -0,0 +1,64 @@
+using Enzyme
+import .EnzymeRules: forward, reverse, augmented_primal
+using .EnzymeRules
+
+include("get_div_grad.jl")
+include("utils.jl")
+
+@testset "$solver" for solver = (Krylov.cg, Krylov.gmres, Krylov.bicgstab)
+    function sparse_laplacian(n :: Int=16; FC=Float64)
+    A = get_div_grad(n, n, n)
+    b = ones(n^3)
+    return A, b
+    end
+
+    A, b = sparse_laplacian(4, FC=Float64)
+    denseA = Matrix(A)
+    fdm = central_fdm(8, 1);
+    function A_one_one(x)
+        _A = copy(denseA)
+        _A[1,1] = x
+        solver(_A,b)
+    end
+
+    function b_one(x)
+        _b = copy(b)
+        _b[1] = x
+        solver(denseA,_b)
+    end
+
+    fda = FiniteDifferences.jacobian(fdm, a -> A_one_one(a)[1], copy(denseA[1,1]))
+    fdb = FiniteDifferences.jacobian(fdm, a -> b_one(a)[1], copy(b[1]))
+    fd =fda[1] + fdb[1]
+    # Test forward
+    ddA = Duplicated(denseA, zeros(size(denseA)))
+    ddb = Duplicated(b, zeros(length(b)))
+    ddA.dval[1,1] = 1.0
+    ddb.dval[1] = 1.0
+    ddx = Enzyme.autodiff(
+        Forward,
+        solver,
+        ddA,
+        ddb
+    )
+    @test isapprox(ddx[1][1], fd, atol=1e-4, rtol=1e-4)
+    # Test reverse
+    function driver!(x, A, b)
+        x .= gmres(A,b)[1]
+        nothing
+    end
+    ddA = Duplicated(denseA, zeros(size(denseA)))
+    ddb = Duplicated(b, zeros(length(b)))
+    ddx = Duplicated(zeros(length(b)), zeros(length(b)))
+    ddx.dval[1] = 1.0
+    Enzyme.autodiff(
+        Reverse,
+        driver!,
+        ddx,
+        ddA,
+        ddb
+    )
+
+    @test isapprox(ddb.dval[1], fdb[1][1], atol=1e-4, rtol=1e-4)
+    @test isapprox(ddA.dval[1,1], fda[1][1], atol=1e-4, rtol=1e-4)
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index e9ee66b..ddcdbbb 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -13,4 +13,7 @@ rtol = 0.0
     @testset "ForwardDiff" begin
         include("forwarddiff.jl")
     end
+    @testset "Enzyme" begin
+        include("enzymediff.jl")
+    end
 end