diff --git a/Project.toml b/Project.toml
index 79902d9..e53ebb6 100644
--- a/Project.toml
+++ b/Project.toml
@@ -11,7 +11,7 @@ Preferences = "21216c6a-2e73-6563-6e65-726566657250"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 
 [compat]
-AbstractFFTs = "1.0"
+AbstractFFTs = "1.5"
 FFTW_jll = "3.3.9"
 MKL_jll = "2019.0.117, 2020, 2021, 2022, 2023"
 Preferences = "1.2"
diff --git a/src/dct.jl b/src/dct.jl
index cd3ec60..a921731 100644
--- a/src/dct.jl
+++ b/src/dct.jl
@@ -171,3 +171,5 @@ end
     mul!(Array{T}(undef, p.plan.osz), p, copy(x)) # need copy to preserve input
 
 *(p::DCTPlan{T,K,true}, x::StridedArray{T}) where {T,K} = mul!(x, p, x)
+
+AbstractFFTs.AdjointStyle(::DCTPlan) = AbstractFFTs.UnitaryAdjointStyle()
diff --git a/src/fft.jl b/src/fft.jl
index daa5866..4831a18 100644
--- a/src/fft.jl
+++ b/src/fft.jl
@@ -1049,3 +1049,9 @@ function *(p::r2rFFTWPlan{T,K,true}, x::StridedArray{T}) where {T,K}
     unsafe_execute!(p, x, x)
     return x
 end
+
+#######################################################################
+
+AbstractFFTs.AdjointStyle(::cFFTWPlan) = AbstractFFTs.FFTAdjointStyle()
+AbstractFFTs.AdjointStyle(::rFFTWPlan{T, FORWARD}) where {T} = AbstractFFTs.RFFTAdjointStyle()
+AbstractFFTs.AdjointStyle(p::rFFTWPlan{T, BACKWARD}) where {T} = AbstractFFTs.IRFFTAdjointStyle(p.osz[first(p.region)])
diff --git a/test/runtests.jl b/test/runtests.jl
index 301194d..981f3f1 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -577,3 +577,27 @@ end
         end
     end
 end
+
+@testset "DCT adjoints" begin
+    # only test on FFTW because MKL is missing functionality
+    if FFTW.get_provider() == "fftw"
+        for x in (randn(3), randn(4), randn(3, 4), randn(3, 4, 5))
+            y = randn(size(x))
+            N = ndims(x)
+            for dims in unique((1, 1:N, N))
+                for P in (plan_dct(x, dims), plan_idct(x, dims))
+                    AbstractFFTs.TestUtils.test_plan_adjoint(P, x)
+                end
+            end
+        end
+    end
+end
+
+@testset "AbstractFFTs FFT backend tests" begin
+    # note this also tests adjoint functionality for FFT plans
+    # only test on FFTW because MKL is missing functionality
+    if FFTW.get_provider() == "fftw"
+        AbstractFFTs.TestUtils.test_complex_ffts(Array)
+        AbstractFFTs.TestUtils.test_real_ffts(Array; copy_input=true)
+    end
+end