ATP synthase (F1Fo-ATPase) catalyses the production of ATP from ADP and orthophosphate by using the proton motive force established across a membrane by photosynthesis or oxidative phosphorylation. The ATP synthase of eukaryotic mitochondria is located in the inner membrane and is comprised of two domains. The globular F1 domain protrudes into the matrix and it contains the catalytic sites for ATP synthesis. The membrane bound Fo domain contains a proton channel. The two domains are connected by central and peripheral stalks. When F1 is removed from the complex, it can hydrolyse ATP but not synthesise it. It is composed of nine subunits with the stoichiometry α3β3γδε . The α and β subunits are arranged alternately round the symmetric γ subunit, which, with the δ and ε subunits, forms the central stalk. Catalysis occurs by a rotary mechanism where rotation in Fo, induced by the passage of protons, is transmitted to F1 via the central stalk. The rotation of the γ subunit induces conformational changes in the catalytic β subunits that lead to the synthesis of ATP. The three catalytic sites proceed through three major and well defined conformations sequentially, and no two sites are the same at any one time. The peripheral stalk counters the tendency of the α3β3 subcomplex to rotate with the γ subunit. The ATP synthase of mitochondria is regulated by an inhibitor protein, IF1, that prevents hydrolysis of ATP when the proton motive force collapses. Saccharomyces cerevisiae has two inhibitor proteins, YIF1 and STF1. The states of oligomerisation of their active and inactive forms have been investigated. In contrast to bovine IF1, which is active as a dimer, the yeast inhibitors are active as monomers around pH 7.0. Like the bovine protein, they form inactive oligomers at higher pH values. While many of features of the mechanism of catalysis of the ATP synthase are well understood, it is now clear that there are many sub-steps within the cycle. Some of them have been revealed by analogues of phosphoryl transfer. Bovine mitochondrial F1-ATPase inhibited with ADP and magnesium fluoride forms a transition state analogue complex. Its structure was solved to 2.5 Å resolution. The βTP and βDP catalytic sites both contain ADP and MgF3 -. The βE subunit binds ADP, despite being in an essentially open conformation. The structure represents a new sub-step in the catalytic cycle just before the release of the substrates of ATP hydrolysis.