  A submanifold of a Riemannian manifold is called a parallel submanifold if
its second fundamental form is parallel with respect to the van der
Waerden-Bortolotti connection. From submanifold point of view, parallel
submanifolds are the simplest Riemannian submanifolds next to totally geodesic
ones. Parallel submanifolds form an important class of Riemannian submanifolds
since extrinsic invariants of a parallel submanifold do not vary from point to
point. In this paper we provide a comprehensive survey on this important class
of submanifolds.
