  A polyhedral product is a natural subspace of a Cartesian product that is
specified by a simplicial complex. The modern formalism arose as a
generalization of the spaces known as moment-angle complexes which were
developed within the nascent subject of toric topology. This field, which began
as a topological approach to toric geometry and aspects of symplectic geometry,
has expanded rapidly in recent years. The investigation of polyhedral products
and their homotopy theoretic properties has developed to the point where they
are studied in various fields of mathematics far removed from their origin. In
this survey, we provide a brief historical overview of the development of this
subject, summarize many of the main results and describe applications.
