diff --git a/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorBase.td b/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorBase.td
--- a/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorBase.td
+++ b/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorBase.td
@@ -15,14 +15,51 @@
   let name = "sparse_tensor";
   let cppNamespace = "::mlir::sparse_tensor";
   let description = [{
-    The `sparse tensor` dialect is intended to hold primitives that
-    form a bridge between high-level operations on sparse tensors
-    and lower-level operations on the actual sparse storage schemes
-    consisting of pointers, indices, and values. This bridge
-    simplifies a `sparse compiler` pass by postponing actual
-    code generation for the supported primitives to a later phase,
-    either by generating calls into a runtime support library
-    or by further lowering the primitives into actual code.
+    The `SparseTensor` dialect supports all the attributes, types,
+    operations, and passes that are required to make sparse tensor
+    types first class citizens within the MLIR compiler infrastructure.
+    The dialect forms a bridge between high-level operations on sparse
+    tensors types and lower-level operations on the actual sparse storage
+    schemes consisting of pointers, indices, and values. Lower-level
+    support may consist of fully generated code or may be provided by
+    means of a small sparse runtime support library.
+
+    The concept of **treating sparsity as a property, not a tedious
+    implementation detail**, by letting a **sparse compiler** generate
+    sparse code automatically was pioneered for dense linear algebra by
+    [Bik96] in MT1 (see https://www.aartbik.com/sparse.php) and formalized
+    to tensor algebra by [Kjolstad17,Kjolstad20] in the Sparse Tensor
+    Algebra Compiler (TACO) project (see http://tensor-compiler.org/).
+
+    The MLIR implementation closely follows the "sparse iteration theory"
+    that forms the foundation of TACO. A rewriting rule is applied to each
+    tensor expression in the Linalg dialect (MLIR's tensor index notation)
+    where the sparsity of tensors is indicated using the per-dimension level
+    types dense/compressed together with a specification of the order on the
+    dimensions (see [Chou18] for an in-depth discussions and possible
+    extensions to these level types). Subsequently, a topologically sorted
+    iteration graph, reflecting the required order on indices with respect
+    to the dimensions of each tensor, is constructed to ensure that all tensors
+    are visited in natural index order. Next, iteration lattices are
+    constructed for the tensor expression for every index in topological
+    order. Each iteration lattice point consists of a conjunction of tensor
+    indices together with a tensor (sub)expression that needs to be evaluated
+    for that conjunction.  Within the lattice, iteration points are ordered
+    according to the way indices are exhausted. As such these iteration
+    lattices drive actual sparse code generation, which consists of a
+    relatively straightforward one-to-one mapping from iteration lattices
+    to combinations of for-loops, while-loops, and if-statements.
+
+    * [Bik96] Aart J.C. Bik. Compiler Support for Sparse Matrix Computations.
+    PhD thesis, Leiden University, May 1996.
+    * [Kjolstad17] Fredrik Berg Kjolstad, Shoaib Ashraf Kamil, Stephen Chou, David
+    Lugato, and Saman Amarasinghe. The Tensor Algebra Compiler. Proceedings of
+    the ACM on Programming Languages, October 2017.
+    * [Kjolstad20] Fredrik Berg Kjolstad. Sparse Tensor Algebra Compilation.
+    PhD thesis, MIT, February, 2020.
+    * [Chou18] Stephen Chou, Fredrik Berg Kjolstad, and Saman Amarasinghe.
+    Format Abstraction for Sparse Tensor Algebra Compilers. Proceedings of
+    the ACM on Programming Languages, October 2018.
   }];
 }
 
diff --git a/mlir/lib/Dialect/SparseTensor/Transforms/Sparsification.cpp b/mlir/lib/Dialect/SparseTensor/Transforms/Sparsification.cpp
--- a/mlir/lib/Dialect/SparseTensor/Transforms/Sparsification.cpp
+++ b/mlir/lib/Dialect/SparseTensor/Transforms/Sparsification.cpp
@@ -6,39 +6,8 @@
 //
 //===----------------------------------------------------------------------===//
 //
-// This file implements lowering sparse tensor types to actual sparse code.
+// This file implements converting sparse tensor types to actual sparse code.
 //
-// The concept of letting a compiler generate sparse code automatically was
-// pioneered for dense linear algebra code in Fortran by [Bik96] in MT1 and
-// formalized to tensor algebra by [Kjolstad17,20] for the Sparse Tensor
-// Algebra Compiler (TACO). The implementation in this file closely follows
-// the "sparse iteration theory" that forms the foundation of TACO. A rewriting
-// rule is applied to each tensor expression in linalg (MLIR's tensor index
-// notation) where the sparsity of tensors is indicated with annotation using
-// a per-dimension specification of sparse/dense storage together with a
-// specification of the order on the dimensions. Subsequently, a topologically
-// sorted iteration graph, reflecting the required order on indices with respect
-// to the dimensions of each tensor, is constructed to ensure that all tensors
-// are visited in natural index order. Next, iteration lattices are constructed
-// for the tensor expression for every index in topological order. Each
-// iteration lattice point consists of a conjunction of tensor indices together
-// with a tensor (sub)expression that needs to be evaluated for that
-// conjunction. Within the lattice, iteration points are ordered according to
-// the way indices are exhausted. As such these iteration lattices drive actual
-// sparse code generation, which consists of a tedious but relatively
-// straightforward one-to-one mapping from iteration lattices to combinations
-// of for-loops, while-loops, and if-statements.
-//
-// [Bik96] Aart J.C. Bik. Compiler Support for Sparse Matrix Computations.
-// PhD thesis, Leiden University, May 1996 (aartbik.com/sparse.php).
-// [Kjolstad17] Fredrik Berg Kjolstad, Shoaib Ashraf Kamil, Stephen Chou,
-// David Lugato, and Saman Amarasinghe. The Tensor Algebra Compiler.
-// Proceedings of the ACM on Programming Languages, October 2017.
-// [Kjolstad20] Fredrik Berg Kjolstad. Sparse Tensor Algebra Compilation.
-// PhD thesis, MIT, February, 2020 (tensor-compiler.org).
-//
-// Implementation detail: We use llvm::SmallVector for vectors with
-// variable lengths and std::vector for vectors with fixed lengths.
 //===----------------------------------------------------------------------===//
 
 #include "mlir/Dialect/Linalg/IR/LinalgOps.h"