diff --git a/NEWS.md b/NEWS.md
index 98c68b32b7a26..6b0af2276db11 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -130,6 +130,7 @@ Standard library changes
 #### SparseArrays
 
 * Display large sparse matrices with a Unicode "spy" plot of their nonzero patterns, and display small sparse matrices by an `Matrix`-like 2d layout of their contents.
+* `issparse` now applies consistently to all wrapper arrays, including nested, by checking `issparse` on the wrapped parent array ([#37644]).
 
 #### Dates
 * `Quarter` period is defined ([#35519]).
diff --git a/stdlib/SparseArrays/src/abstractsparse.jl b/stdlib/SparseArrays/src/abstractsparse.jl
index 3886fa001c93e..93fc59bcd622f 100644
--- a/stdlib/SparseArrays/src/abstractsparse.jl
+++ b/stdlib/SparseArrays/src/abstractsparse.jl
@@ -50,17 +50,19 @@ julia> issparse(Array(sv))
 false
 ```
 """
-issparse(A::AbstractArray) = false
+function issparse(A::AbstractArray)
+    # Handle wrapper arrays: sparse if it is wrapping a sparse array.
+    # This gets compiled away during specialization.
+    p = parent(A)
+    if p === A
+        # have reached top of wrapping without finding a sparse array, assume it is not.
+        return false
+    else
+        return issparse(p)
+    end
+end
+issparse(A::DenseArray) = false
 issparse(S::AbstractSparseArray) = true
-issparse(S::LinearAlgebra.Adjoint{<:Any,<:AbstractSparseArray}) = true
-issparse(S::LinearAlgebra.Transpose{<:Any,<:AbstractSparseArray}) = true
-
-issparse(S::LinearAlgebra.Symmetric{<:Any,<:AbstractSparseMatrix}) = true
-issparse(S::LinearAlgebra.Hermitian{<:Any,<:AbstractSparseMatrix}) = true
-issparse(S::LinearAlgebra.LowerTriangular{<:Any,<:AbstractSparseMatrix}) = true
-issparse(S::LinearAlgebra.UnitLowerTriangular{<:Any,<:AbstractSparseMatrix}) = true
-issparse(S::LinearAlgebra.UpperTriangular{<:Any,<:AbstractSparseMatrix}) = true
-issparse(S::LinearAlgebra.UnitUpperTriangular{<:Any,<:AbstractSparseMatrix}) = true
 
 indtype(S::AbstractSparseArray{<:Any,Ti}) where {Ti} = Ti
 
diff --git a/stdlib/SparseArrays/test/sparse.jl b/stdlib/SparseArrays/test/sparse.jl
index 79e5a98d6bc22..b505233ab9b2c 100644
--- a/stdlib/SparseArrays/test/sparse.jl
+++ b/stdlib/SparseArrays/test/sparse.jl
@@ -2114,6 +2114,11 @@ end
     @test issparse(LinearAlgebra.UnitLowerTriangular(Array(m))) == false
     @test issparse(UpperTriangular(Array(m))) == false
     @test issparse(LinearAlgebra.UnitUpperTriangular(Array(m))) == false
+    @test issparse(Base.ReshapedArray(m, (20, 5), ()))
+
+    # greater nesting
+    @test issparse(Symmetric(UpperTriangular(m)))
+    @test issparse(Symmetric(UpperTriangular(Array(m)))) == false
 end
 
 @testset "issparse for sparse vectors #34253" begin