This review outlines developments in the growth of crystalline oxides on the ubiquitous silicon semiconductor platform. The overall goal of this endeavor is the integration of multifunctional complex oxides with advanced semiconductor technology. Oxide epitaxy in materials systems achieved through conventional deposition techniques is described first, followed by a description of the science and technology of using atomic layer-by-layer deposition with molecular beam epitaxy (MBE) to systematically construct the oxide–silicon interface. An interdisciplinary approach involving MBE, advanced real-space structural characterization, and first-principles theory has led to a detailed understanding of the process by which the interface between crystalline oxides and silicon forms, the resulting structure of the interface, and the link between structure and functionality. Potential applications in electronics and photonics are also discussed.