This chapter reviews the various fundamental unstable and stable splitting theorems for the polyhedral product. It presents results on the cohomology of polyhedral products. The chapter describes the application of polyhedral products to questions concerning the Golod properties of certain rings. It discusses higher Whitehead products, constructed using polyhedral products. A polyhedral product is a natural topological subspace of a Cartesian product, determined by a simplicial complex K and a family of pointed pairs of spaces, one for each vertex of K. The development of the theory of polyhedral products was guided by their inextricable link to spaces known as moment–angle manifolds which arose within the subject of toric topology. Higher Whitehead products were introduced into the homotopy theory of moment–angle complexes in the work of T. Panov and N. Ray.