Over the past several years, topological insulators have become an intensively researched topic in condensed matter physics. Interest in these materials stems not only from their being a fundamentally new phase of quantum matter, but also because they hold promise for novel technological applications ranging from low power spin-based electronics to fault-tolerant quantum computers. In this talk, I will describe the early theoretical and experimental works that established the existence of topological insulators. In particular, I will focus on the role that spin- and angle-resolved photoemission spectroscopy played in the discovery of topological insulators in three-dimensional bulk crystals. Finally I will discuss some of the exciting new research directions that topological insulators have generated.