Polyhedral products provide a natural unifying framework for many familiar constructions in topology (products, wedges, joins), as well as less familiar ones (moment-angle manifolds, Davis-Januszkiewicz spaces) which have been intensively studied from a homotopy theoretic point of view in recent years. These lectures will survey some fundamental results surrounding the topology of polyhedral products with an emphasis on their connections to toric topology, combinatorics, commutative algebra, and geometric group theory. Topics will include the cohomology of moment-angle complexes, the Bahri-Bendersky-Cohen-Gitler suspension splitting, polyhedral product models of classifying spaces, and the Charney-Davis conjecture.