A renewal of interest in molecular beam epitaxy (MBE) of complex metal oxides has occurred in recent years. This revival of interest is due in part to advances in the technology of MBE oxide epitaxy and in part to the potential of such materials for insertion into unique applications. Some of the key advances in oxide epitaxy are reviewed, including dramatic quality improvement in complex oxides, particularly the perovskite oxide class. Some of the latter advances include high quality integration of perovskites on silicon pioneered by McKee et al. [Phys. Rev. Lett. 81, 3014 (1998)] and demonstration of interface charge control and oxide-oxide heterointerfaces with mobility exceeding 10 000 cm (2)/V s by Huang et al. [Physica E 22 712 (2004)]. A new demonstration of LiNbO3 epitaxy on SiC using a novel chemistry will also be detailed. Whether it is applications in mainstream silicon such as alternative gate dielectric replacements or scarcely examined multifunctional oxides, MBE holds promise for a variety of applications. It is shown that MBE affords unique advantages, particularly in the crucial areas of stoichiometry control and deposition uniformity, while offering significant challenges in areas such as growth rate and, in limited cases, interfacial chemistry control. Recent advances in oxide MBE component technology are briefly examined including a method for eliminating electron beam evaporation of refractory metals in certain applications. Potential applications are highlighted and critical challenges are identified. (c) 2005 American Vacuum Society.