The confluence of state-of-the-art electronic-structure computations and modern synthetic materials growth techniques is proving indispensable in the search for and discovery of new functionalities in oxide thin films and heterostructures. Here, we review the recent contributions of electronic-structure calculations to predicting, understanding, and discovering new materials physics in thin-film perovskite oxides. We show that such calculations can accurately predict both structure and properties in advance of film synthesis, thereby guiding the search for materials combinations with specific targeted functionalities. In addition, because they can isolate and decouple the effects of various parameters which unavoidably occur simultaneously in an experiment-such as epitaxial strain, interfacial chemistry and defect profiles-they are able to provide new fundamental knowledge about the underlying physics. We conclude by outlining the limitations of current computational techniques, as well as some important open questions that we hope will motivate further methodological developments in the field.