Functional oxides are an untapped resource for futuristic devices and functionalities. These functionalities can range from high temperature superconductivity to multiferroicity and novel catalytic schemes. The most prominent route for transforming these ideas from a single device in the lab to practical technologies is by integration with semiconductors. Moreover, coupling oxides with semiconductors can herald new and unexpected functionalities that exist in neither of the individual materials. Therefore, oxide epitaxy on semiconductors provides a materials platform for novel device technologies. As oxides and semiconductors exhibit properties that are complementary to one another, epitaxial heterostructures comprised of the two are uniquely poised to deliver rich functionalities. This review discusses recent advancements in the growth of epitaxial oxides on semiconductors, and the electronic and physical structure of their interfaces. Leaning on these fundamentals and practicalities, the material behavior and functionality of semiconductor-oxide heterostructures is discussed, and their potential as device building blocks is highlighted. The culmination of this discussion is a review of recent advances in the development of prototype devices based on semiconductor-oxide heterostructures, in areas ranging from silicon photonics to photocatalysis. This overview is intended to stimulate ideas for new concepts of functional devices and lay the groundwork for their realization.