Quantum wells created from nanostructured transition metal oxides offer unique possibilities for creating and manipulating quantum states of matter, including novel superconductors, high Curie temperature magnets, controllable metal-insulator transitions, and new topological states. This article explores what is known and conjectured about confined electronic states in oxide quantum wells. Theoretical challenges are reviewed, along with issues arising in the creation of oxide quantum wells. Examples from the current experimental state of the art are summarized, open questions are discussed, and prospects for the future are outlined. The key roles of epitaxial strain and proximity effects are emphasized.