We review recent advances in understanding of the structure of the F₁F₀-ATP synthase of the mitochondrial inner membrane (mtATPase). A significant achievement has been the determination of the structure of the principal peripheral or stator stalk components bringing us closer to achieving the Holy Grail of a complete 3D structure for the complex. A major focus of the field in recent years has been to understand the physiological significance of dimers or other oligomer forms of mtATPase recoverable from membranes and their relationship to the structure of the cristae of the inner mitochondrial membrane. In addition, the association of mtATPase with other membrane proteins has been described and suggests that further levels of functional organization need to be considered. Many reports in recent years have concerned the location and function of ATP synthase complexes or its component subunits on the external surface of the plasma membrane. We consider whether the evidence supports complete complexes being located on the cell surface, the biogenesis of such complexes, and aspects of function especially related to the structure of mtATPase.