Molecular-beam epitaxy (MBE) is the “gold standard” synthesis technique for preparing semiconductor heterostructures with high purity, high mobility, and exquisite control of layer thickness at the atomic-layer level. Its use for the growth of multicomponent oxides got off to a rocky start 30 yr ago, but in the ensuing decades, it has become the definitive method for the preparation of oxide heterostructures too, particularly when it is desired to explore their intrinsic properties. Examples illustrating the unparalleled achievements of oxide MBE are given; these motivate its expanding use for exploring the potentially revolutionary states of matter possessed by oxide systems.