diff --git a/Project.toml b/Project.toml
index 217ab01a4..51815a84c 100644
--- a/Project.toml
+++ b/Project.toml
@@ -31,6 +31,7 @@ UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 
 [weakdeps]
 AMDGPU = "21141c5a-9bdb-4563-92ae-f87d6854732e"
+AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
 Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
 DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
@@ -44,6 +45,7 @@ Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 PythonCall = "6099a3de-0909-46bc-b1f4-468b9a2dfc0d"
 
 [extensions]
+AbstractFFTsExt = "AbstractFFTs"
 CUDAExt = "CUDA"
 DistributionsExt = "Distributions"
 GraphVizExt = "GraphViz"
@@ -58,6 +60,7 @@ ROCExt = "AMDGPU"
 
 [compat]
 AMDGPU = "1"
+AbstractFFTs = "1.5.0"
 Adapt = "4"
 CUDA = "3, 4, 5"
 Colors = "0.12, 0.13"
diff --git a/docs/src/darray.md b/docs/src/darray.md
index 715a6cbe8..e813bfeda 100644
--- a/docs/src/darray.md
+++ b/docs/src/darray.md
@@ -447,3 +447,7 @@ From `LinearAlgebra`:
 - `mul!` (In-place Matrix-Matrix multiply)
 - `cholesky`/`cholesky!` (In-place/Out-of-place Cholesky factorization)
 - `lu`/`lu!` (In-place/Out-of-place LU factorization (`NoPivot` only))
+
+From `AbstractFFTs`:
+- `fft`/`fft!`
+- `ifft`/`ifft!`
\ No newline at end of file
diff --git a/ext/AbstractFFTsExt.jl b/ext/AbstractFFTsExt.jl
new file mode 100644
index 000000000..5f24ba584
--- /dev/null
+++ b/ext/AbstractFFTsExt.jl
@@ -0,0 +1,320 @@
+module AbstractFFTsExt
+
+import Dagger
+import Dagger: DArray, DVector, DMatrix, Blocks, AutoBlocks, InOut
+import AbstractFFTs
+import LinearAlgebra
+
+abstract type Decomposition end
+struct Pencil <: Decomposition end
+struct Slab <: Decomposition end
+
+# High-level interface
+
+## TODO: Add optimized 1D algorithm
+
+## 1D out-of-place
+AbstractFFTs.fft(A::DVector) = DVector(AbstractFFTs.fft(collect(A)))
+AbstractFFTs.ifft(A::DVector) = DVector(AbstractFFTs.ifft(collect(A)))
+
+## 1D in-place
+function AbstractFFTs.fft!(DA::DVector{T}) where T
+    A = Vector{T}(undef, length(DA))
+    copyto!(A, DA)
+    AbstractFFTs.fft!(A)
+    copyto!(DA, A)
+    return DA
+end
+function AbstractFFTs.ifft!(DA::DVector{T}) where T
+    A = Vector{T}(undef, length(DA))
+    copyto!(A, DA)
+    AbstractFFTs.ifft!(A)
+    copyto!(DA, A)
+    return DA
+end
+
+## 2D out-of-place
+function AbstractFFTs.fft(DA::DMatrix, dims=(1, 2))
+    DB = similar(DA)
+    _fft!(DB, DA, dims)
+    return DB
+end
+function AbstractFFTs.ifft(DA::DMatrix, dims=(1, 2))
+    DB = similar(DA)
+    _ifft!(DB, DA, dims)
+    return DB
+end
+
+## 2D in-place
+function AbstractFFTs.fft!(DA::DMatrix{T}, dims=(1, 2)) where T
+    _fft!(DA, DA, dims)
+    return DA
+end
+function AbstractFFTs.ifft!(DA::DMatrix{T}, dims=(1, 2)) where T
+    _ifft!(DA, DA, dims)
+    return DA
+end
+
+## 3D out-of-place
+function AbstractFFTs.fft(DA::DArray{T,3}, dims=(1, 2, 3); decomp::Union{Decomposition,Symbol}=Pencil()) where T
+    DB = similar(DA)
+    _decomp = _to_decomp(decomp)
+    _fft!(DB, DA, dims; decomp=_decomp)
+    return DB
+end
+function AbstractFFTs.ifft(DA::DArray{T,3}, dims=(1, 2, 3); decomp::Union{Decomposition,Symbol}=Pencil()) where T
+    DB = similar(DA)
+    _decomp = _to_decomp(decomp)
+    _ifft!(DB, DA, dims; decomp=_decomp)
+    return DB
+end
+
+## 3D in-place
+function AbstractFFTs.fft!(DA::DArray{T,3}, dims=(1, 2, 3); decomp::Union{Decomposition,Symbol}=Pencil()) where T
+    _decomp = _to_decomp(decomp)
+    _fft!(DA, DA, dims; decomp=_decomp)
+    return DA
+end
+function AbstractFFTs.ifft!(DA::DArray{T,3}, dims=(1, 2, 3); decomp::Union{Decomposition,Symbol}=Pencil()) where T
+    _decomp = _to_decomp(decomp)
+    _ifft!(DA, DA, dims; decomp=_decomp)
+    return DA
+end
+
+# Mid-level interface
+
+_to_decomp(decomp::Decomposition) = decomp
+function _to_decomp(decomp::Symbol)
+    if decomp == :pencil
+        return Pencil()
+    elseif decomp == :slab
+        return Slab()
+    else
+        throw(ArgumentError("Unknown decomposition type: $decomp\nSupported types: :pencil, :slab"))
+    end
+end
+
+## 2D
+function _fft!(output::DMatrix{T}, input::DMatrix{T}, dims=(1, 2)) where T
+    N = size(input, 1)
+    np = length(Dagger.compatible_processors())
+    A = zeros(Blocks(N, div(N, np)), T, size(input))
+    copyto!(A, input)
+    B = zeros(Blocks(div(N, np), N), T, size(input))
+    __fft!(A, B, dims)
+    copyto!(output, B)
+    return output
+end
+function _ifft!(output::DMatrix{T}, input::DMatrix{T}, dims=(1, 2)) where T
+    N = size(input, 1)
+    np = length(Dagger.compatible_processors())
+    A = zeros(Blocks(N, div(N, np)), T, size(input))
+    copyto!(A, input)
+    B = zeros(Blocks(div(N, np), N), T, size(input))
+    __ifft!(A, B, dims)
+    copyto!(output, B)
+    return output
+end
+
+## 3D
+function _fft!(output::DArray{T,3}, input::DArray{T,3}, dims=(1, 2, 3); decomp::Decomposition=Pencil()) where T
+    N = size(input, 1)
+    np = length(Dagger.compatible_processors())
+    if decomp isa Pencil
+        A = zeros(Blocks(N, div(N, np), div(N, np)), T, size(input))
+        B = zeros(Blocks(div(N, np), N, div(N, np)), T, size(input))
+        C = zeros(Blocks(div(N, np), div(N, np), N), T, size(input))
+        copyto!(A, input)
+        __fft!(decomp, A, B, C, dims)
+        copyto!(output, C)
+        return output
+    elseif decomp isa Slab
+        A = zeros(Blocks(N, N, div(N, np)), T, size(input))
+        B = zeros(Blocks(div(N, np), div(N, np), N), T, size(input))
+        copyto!(A, input)
+        __fft!(decomp, A, B, dims)
+        copyto!(output, B)
+        return output
+    else
+        throw(ArgumentError("Unknown decomposition type: $decomp"))
+    end
+end
+function _ifft!(output::DArray{T,3}, input::DArray{T,3}, dims=(1, 2, 3); decomp::Decomposition=Pencil()) where T
+    N = size(input, 1)
+    np = length(Dagger.compatible_processors())
+    if decomp isa Pencil
+        A = zeros(Blocks(div(N, np), div(N, np), N), T, size(input))
+        B = zeros(Blocks(div(N, np), N, div(N, np)), T, size(input))
+        C = zeros(Blocks(N, div(N, np), div(N, np)), T, size(input))
+        copyto!(A, input)
+        __ifft!(decomp, A, B, C, dims)
+        copyto!(output, C)
+        return output
+    elseif decomp isa Slab
+        A = zeros(Blocks(div(N, np), div(N, np), N), T, size(input))
+        B = zeros(Blocks(N, N, div(N, np)), T, size(input))
+        copyto!(A, input)
+        __ifft!(decomp, A, B, dims)
+        copyto!(output, B)
+        return output
+    end
+end
+
+# Internal functions
+
+struct FFT! end
+struct RFFT! end
+struct IRFFT! end
+struct IFFT! end
+
+function plan_transform(transform, A, dims; kwargs...)
+    if transform isa FFT!
+        AbstractFFTs.plan_fft!(A, dims; kwargs...)
+    elseif transform isa IFFT!
+        AbstractFFTs.plan_ifft!(A, dims; kwargs...)
+    else
+        throw(ArgumentError("Unknown transform type: $transform"))
+    end
+end
+function apply_fft!(out_part, in_part, transform, dim)
+    plan = plan_transform(transform, in_part, dim)
+    LinearAlgebra.mul!(out_part, plan, in_part)
+    return
+end
+apply_fft!(inout_part, transform, dim) = apply_fft!(inout_part, inout_part, transform, dim)
+
+## 2D
+function __fft!(A::DMatrix{T}, B::DMatrix{T}, dims) where T
+    A_parts = A.chunks
+    B_parts = B.chunks
+
+    Dagger.spawn_datadeps() do
+        for idx in eachindex(A_parts)
+            Dagger.@spawn name="apply_fft!(dim 1)" apply_fft!(InOut(A_parts[idx]), FFT!(), dims[1])
+        end
+    end
+
+    copyto!(B, A)
+    Dagger.spawn_datadeps() do
+        for idx in eachindex(B_parts)
+            Dagger.@spawn name="apply_fft!(dim 2)" apply_fft!(InOut(B_parts[idx]), FFT!(), dims[2])
+        end
+    end
+
+    return
+end
+function __ifft!(A::DMatrix{T}, B::DMatrix{T}, dims) where T
+    A_parts = A.chunks
+    B_parts = B.chunks
+
+    Dagger.spawn_datadeps() do
+        for idx in eachindex(A_parts)
+            Dagger.@spawn name="apply_ifft!(dim 1)" apply_fft!(InOut(A_parts[idx]), IFFT!(), dims[1])
+        end
+    end
+
+    copyto!(B, A)
+    Dagger.spawn_datadeps() do
+        for idx in eachindex(B_parts)
+            Dagger.@spawn name="apply_ifft!(dim 2)" apply_fft!(InOut(B_parts[idx]), IFFT!(), dims[2])
+        end
+    end
+
+    return
+end
+
+## 3D
+function __fft!(::Pencil, A::DArray{T,3}, B::DArray{T,3}, C::DArray{T,3}, dims) where T
+    A_parts = A.chunks
+    B_parts = B.chunks
+    C_parts = C.chunks
+
+    Dagger.spawn_datadeps() do
+        for idx in eachindex(A_parts)
+            Dagger.@spawn name="apply_fft!(dim 1)" apply_fft!(InOut(A_parts[idx]), FFT!(), dims[1])
+        end
+    end
+
+    copyto!(B, A)
+    Dagger.spawn_datadeps() do
+        for idx in eachindex(B_parts)
+            Dagger.@spawn name="apply_fft!(dim 2)" apply_fft!(InOut(B_parts[idx]), FFT!(), dims[2])
+        end
+    end
+
+    copyto!(C, B)
+    Dagger.spawn_datadeps() do
+        for idx in eachindex(C_parts)
+            Dagger.@spawn name="apply_fft!(dim 3)" apply_fft!(InOut(C_parts[idx]), FFT!(), dims[3])
+        end
+    end
+
+    return
+end
+function __fft!(::Slab, A::DArray{T,3}, B::DArray{T,3}, dims) where T
+    A_parts = A.chunks
+    B_parts = B.chunks
+
+    Dagger.spawn_datadeps() do
+        for idx in eachindex(A_parts)
+            Dagger.@spawn name="apply_fft!(dim 1&2)" apply_fft!(InOut(A_parts[idx]), FFT!(), (dims[1], dims[2]))
+        end
+    end
+
+    copyto!(B, A)
+    Dagger.spawn_datadeps() do
+        for idx in eachindex(B_parts)
+            Dagger.@spawn name="apply_fft!(dim 3)" apply_fft!(InOut(B_parts[idx]), FFT!(), dims[3])
+        end
+    end
+
+    return
+end
+function __ifft!(::Pencil, A::DArray{T,3}, B::DArray{T,3}, C::DArray{T,3}, dims) where T
+    A_parts = A.chunks
+    B_parts = B.chunks
+    C_parts = C.chunks
+
+    Dagger.spawn_datadeps() do
+        for idx in eachindex(A_parts)
+            Dagger.@spawn name="apply_ifft!(dim 3)" apply_fft!(InOut(A_parts[idx]), IFFT!(), dims[3])
+        end
+    end
+
+    copyto!(B, A)
+    Dagger.spawn_datadeps() do
+        for idx in eachindex(B_parts)
+            Dagger.@spawn name="apply_ifft!(dim 2)" apply_fft!(InOut(B_parts[idx]), IFFT!(), dims[2])
+        end
+    end
+
+    copyto!(C, B)
+    Dagger.spawn_datadeps() do
+        for idx in eachindex(C_parts)
+            Dagger.@spawn name="apply_ifft!(dim 1)" apply_fft!(InOut(C_parts[idx]), IFFT!(), dims[1])
+        end
+    end
+
+    return
+end
+function __ifft!(::Slab, A::DArray{T,3}, B::DArray{T,3}, dims) where T
+    A_parts = A.chunks
+    B_parts = B.chunks
+
+    Dagger.spawn_datadeps() do
+        for idx in eachindex(A_parts)
+            Dagger.@spawn name="apply_ifft!(dim 3)" apply_fft!(InOut(A_parts[idx]), IFFT!(), dims[3])
+        end
+    end
+
+    copyto!(B, A)
+    Dagger.spawn_datadeps() do
+        for idx in eachindex(B_parts)
+            Dagger.@spawn name="apply_ifft!(dim 1&2)" apply_fft!(InOut(B_parts[idx]), IFFT!(), (dims[1], dims[2]))
+        end
+    end
+
+    return
+end
+
+end # module AbstractFFTsExt
diff --git a/test/Project.toml b/test/Project.toml
index 10b64f326..72daddfb3 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -5,6 +5,7 @@ CondaPkg = "992eb4ea-22a4-4c89-a5bb-47a3300528ab"
 DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
 Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
 GraphViz = "f526b714-d49f-11e8-06ff-31ed36ee7ee0"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 JSON3 = "0f8b85d8-7281-11e9-16c2-39a750bddbf1"
diff --git a/test/array/fft.jl b/test/array/fft.jl
new file mode 100644
index 000000000..54a4afe2a
--- /dev/null
+++ b/test/array/fft.jl
@@ -0,0 +1,141 @@
+using FFTW
+
+@testset "FFT" begin
+    @testset for T in (ComplexF64, ComplexF32)
+        @testset "1D" begin
+            # Out-of-place
+            A = rand(T, 100)
+            DA = DArray(A)
+            B = fft(A)
+            DB = fft(DA)
+            @test DB isa DVector{T}
+            @test B ≈ collect(DB)
+
+            # In-place
+            A = rand(T, 100)
+            DA = DArray(A)
+            fft!(A)
+            fft!(DA)
+            @test A ≈ collect(DA)
+        end
+
+        @testset "2D" begin
+            # Out-of-place
+            A = rand(T, 100, 100)
+            DA = DArray(A)
+            B = fft(A)
+            DB = fft(DA)
+            @test DB isa DMatrix{T}
+            @test B ≈ collect(DB)
+
+            # In-place
+            A = rand(T, 100, 100)
+            DA = DArray(A)
+            fft!(A)
+            fft!(DA)
+            @test A ≈ collect(DA)
+        end
+
+        @testset "3D" begin
+            # Out-of-place (Pencil)
+            A = rand(T, 100, 100, 100)
+            DA = DArray(A)
+            B = fft(A)
+            DB = fft(DA; decomp=:pencil)
+            @test DB isa DArray{T, 3}
+            @test B ≈ collect(DB)
+
+            # Out-of-place (Slab)
+            A = rand(T, 100, 100, 100)
+            DA = DArray(A)
+            B = fft(A)
+            DB = fft(DA; decomp=:slab)
+            @test DB isa DArray{T, 3}
+            @test B ≈ collect(DB)
+
+            # In-place (Pencil)
+            A = rand(T, 100, 100, 100)
+            DA = DArray(A)
+            fft!(A)
+            fft!(DA; decomp=:pencil)
+            @test A ≈ collect(DA)
+
+            # In-place (Slab)
+            A = rand(T, 100, 100, 100)
+            DA = DArray(A)
+            fft!(A)
+            fft!(DA; decomp=:slab)
+            @test A ≈ collect(DA)
+        end
+    end
+end
+
+@testset "IFFT" begin
+    for T in (ComplexF64, ComplexF32)
+        @testset "1D" begin
+            # Out-of-place
+            A = rand(T, 100)
+            DA = DArray(A)
+            B = ifft(A)
+            DB = ifft(DA)
+            @test DB isa DVector{T}
+            @test B ≈ collect(DB)
+
+            # In-place
+            A = rand(T, 100)
+            DA = DArray(A)
+            ifft!(A)
+            ifft!(DA)
+            @test A ≈ collect(DA)
+        end
+
+        @testset "2D" begin
+            # Out-of-place
+            A = rand(T, 100, 100)
+            DA = DArray(A)
+            B = ifft(A)
+            DB = ifft(DA)
+            @test DB isa DMatrix{T}
+            @test B ≈ collect(DB)
+
+            # In-place
+            A = rand(T, 100, 100)
+            DA = DArray(A)
+            ifft!(A)
+            ifft!(DA)
+            @test A ≈ collect(DA)
+        end
+
+        @testset "3D" begin
+            # Out-of-place (Pencil)
+            A = rand(T, 100, 100, 100)
+            DA = DArray(A)
+            B = ifft(A)
+            DB = ifft(DA; decomp=:pencil)
+            @test DB isa DArray{T, 3}
+            @test B ≈ collect(DB)
+
+            # Out-of-place (Slab)
+            A = rand(T, 100, 100, 100)
+            DA = DArray(A)
+            B = ifft(A)
+            DB = ifft(DA; decomp=:slab)
+            @test DB isa DArray{T, 3}
+            @test B ≈ collect(DB)
+
+            # In-place (Pencil)
+            A = rand(T, 100, 100, 100)
+            DA = DArray(A)
+            ifft!(A)
+            ifft!(DA; decomp=:pencil)
+            @test A ≈ collect(DA)
+
+            # In-place (Slab)
+            A = rand(T, 100, 100, 100)
+            DA = DArray(A)
+            ifft!(A)
+            ifft!(DA; decomp=:slab)
+            @test A ≈ collect(DA)
+        end
+    end
+end
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index a7b7a890a..8ef8cb3a0 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -32,6 +32,7 @@ tests = [
     ("Array - LinearAlgebra - LU", "array/linalg/lu.jl"),
     ("Array - Random", "array/random.jl"),
     ("Array - Stencils", "array/stencil.jl"),
+    ("Array - FFT", "array/fft.jl"),
     ("GPU", "gpu.jl"),
     ("Caching", "cache.jl"),
     ("Disk Caching", "diskcaching.jl"),