This introductory article briefly summarizes how our views about the structural features of ATP synthases (F0F1) have evolved over the past 30 years and also reviews some of our current views in the year 2000 about the structures of these remarkably unique enzyme complexes. Suffice it to say that as we approach the end of the first year of this new millinium, we can be conservatively confident that we have a reasonably good grasp of the overall "low-resolution" structural features of ATP synthases. Electron microscopy techniques, combined with the tools of biochemistry, molecular biology, and immunology, have played the leading role here by identifying the headpiece, basepiece, central stalk, side stalk, cap, and in the mitochondrial enzyme, the collar around the central stalk. We can be reasonably confident also that we have a fairly good grasp of much of the "high-resolution" structural features of both the F1 moiety comprised of fives subunit types (alpha, beta, gamma, delta, and epsilon) and parts of the F0 moiety comprised of either three (E. coli) or at least ten (mitochondria) subunit types. This information acquired in several different laboratories, either by X-ray crystallography or NMR spectroscopy, includes details about the active site and subunit relationships. Moreover, it is consistent with recently reported data that the F1 moiety may be an ATP driven motor, which, during ATP synthesis, is driven in reverse by the electrochemical proton gradient generated by the electron transport chain. The real structural challenges of the future are to acquire at high resolution "complete" ATP synthase complexes representative of different stages of the catalytic cycle during ATP synthesis and representative also of key regulatory states.