Research in ABO3 perovskite oxides ranges from fundamental scientific studies in superconductivity and magnetism to technologies for advanced low-power electronics, energy storage, and conversion. The breadth in functionalities observed in this versatile materials class originates, in part, from the ability to control the local and extended crystallographic structure of corner-connected octahedral units. While an established paradigm exists to alter the size, shape, and connectivity of the octahedral building blocks in bulk materials, these approaches are often limited to certain subsets of the allowed perovskite archetypes and chemistries. In this article, we describe emerging routes in thin films and multilayer superlattices enabled by epitaxial synthesis aimed at engineering the octahedral connectivity—rotational magnitudes and patterns—to reach unexplored portions of the crystallographic structure–property phase space for rational materials design. We review three promising chemistry-independent strategies that provide a handle to tune the octahedral connectivity: epitaxial strain, interfacial control at perovskite/perovskite heterojunctions, and rotation engineering in short-period superlattices. Finally, we touch upon potential new functionalities that could be attained by extending these approaches to static and dynamic manipulation of the perovskite structure through external fields and highlight unresolved questions for the deterministic control of octahedral rotations in perovskite-structured materials.