Abstract: Polyhedral products are topological spaces formed by gluing products of spaces according to the inclusion relation of faces in the underlying simplicial complexes. Examples include Davis-Januszkiewicz spaces and moment-angle complexes. There is a beautiful interplay between their topology and the combinatorial information of simplicial complexes, which makes them important in toric topology, algebraic and combinatorial geometry, geometric group theory and homotopy theory. In this seminar I will talk about the definition of polyhedral products, their functorial properties and how to compute their cohomologies. If time permits, then I will mention my recent work that uses polyhedral products to study the realization problem of graded commutative rings.