diff --git a/Project.toml b/Project.toml
index f56b35ba7..8ca217db8 100644
--- a/Project.toml
+++ b/Project.toml
@@ -18,12 +18,14 @@ TupleTools = "9d95972d-f1c8-5527-a6e0-b4b365fa01f6"
 VectorInterface = "409d34a3-91d5-4945-b6ec-7529ddf182d8"
 
 [weakdeps]
+Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
 cuTENSOR = "011b41b2-24ef-40a8-b3eb-fa098493e9e1"
 
 [extensions]
+TensorKitAdaptExt = "Adapt"
 TensorKitCUDAExt = ["CUDA", "cuTENSOR"]
 TensorKitChainRulesCoreExt = "ChainRulesCore"
 TensorKitFiniteDifferencesExt = "FiniteDifferences"
diff --git a/ext/TensorKitAdaptExt.jl b/ext/TensorKitAdaptExt.jl
new file mode 100644
index 000000000..734f174ad
--- /dev/null
+++ b/ext/TensorKitAdaptExt.jl
@@ -0,0 +1,19 @@
+module TensorKitAdaptExt
+
+using TensorKit
+using TensorKit: AdjointTensorMap
+using Adapt
+
+function Adapt.adapt_structure(to, x::TensorMap)
+    data′ = adapt(to, x.data)
+    return TensorMap{eltype(data′)}(data′, space(x))
+end
+function Adapt.adapt_structure(to, x::AdjointTensorMap)
+    return adjoint(adapt(to, parent(x)))
+end
+function Adapt.adapt_structure(to, x::DiagonalTensorMap)
+    data′ = adapt(to, x.data)
+    return DiagonalTensorMap(data′, x.domain)
+end
+
+end
diff --git a/src/TensorKit.jl b/src/TensorKit.jl
index c35101235..688e7363c 100644
--- a/src/TensorKit.jl
+++ b/src/TensorKit.jl
@@ -142,7 +142,6 @@ using LinearAlgebra: norm, dot, normalize, normalize!, tr,
     eigen, eigen!, svd, svd!,
     isposdef, isposdef!, rank, cond,
     Diagonal, Hermitian
-using MatrixAlgebraKit
 
 import Base.Meta
 
diff --git a/test/cuda/tensors.jl b/test/cuda/tensors.jl
index 8a89a8ad8..e495eef08 100644
--- a/test/cuda/tensors.jl
+++ b/test/cuda/tensors.jl
@@ -115,6 +115,20 @@ for V in spacelist
                 @test domain(t2) == one(W)
             end
         end
+        @timedtestset "Adapt" begin
+            W = V1 ⊗ V2 ⊗ V3 ⊗ V4 ⊗ V5
+            for T in (Int, Float32, ComplexF64)
+                t = rand(T, W)
+                t_gpu = @constinferred adapt(CuArray, t)
+                @test storagetype(t_gpu) <: CuArray{T}
+                @test scalartype(t_gpu) === scalartype(t)
+                @test collect(t_gpu.data) == t.data
+
+                t_cpu = @constinferred adapt(Array, t_gpu)
+                @test t_cpu == t
+                @test storagetype(t_cpu) <: Array{T}
+            end
+        end
         @timedtestset "Tensor Dict conversion" begin
             W = V1 ⊗ V2 ⊗ V3 ← V4 ⊗ V5
             for T in (Int, Float32, ComplexF64)