The isolation of ATP synthase (F0F1) (82) and F0 (83) 34 years ago finally revealed that F0F1 is a motor composed of F0 (ion-motor, abc subunits) and F1 (ATP-motor, alpha 3 beta 3 gamma delta epsilon subunits) (Fig. 1). The single molecule videotape (4, 5, 65, 66) revealed that gamma epsilon axis of F1 rotates counterclockwise, proceeds by each 2 pi/3 step, and is driven by torque of 42 pN.nm (12) with nearly 100% efficiency (5) (Fig. 4). The motor is composed of a rotor (gamma epsilon-F0-c) and a stator (alpha 3 beta 3 delta-F0-ab), and the rotor is connected to a shaft (gamma epsilon). Since F0F1 is driven by delta microH+ (9, 10, 84), biophysical studies on stable TF0F1 (1, 7) are essential to elucidate the mechanism. These include nanomechanics (4, 5) (Fig. 4), crystallography (2, 3) (Figs. 2 and 3), NMR (51, 52), ESR (56), synchrotron analysis (3, 28), and electrophysiology (10, 25). The KmATP value of rotation is 0.8 microM, with the Vmax of 3.9 rps (5). This corresponds to the bi-site catalysis in proton transport by F0F1 (10, 70, 84). X-ray crystallography of MF1 (2) and the alpha 3 beta 3 oligomer of TF1 (3) (Fig. 2) together with mutation analyses revealed the role of residues in the rotation. The idea of elastic energy store is proposed in alpha 3 beta 3 gamma during the stepping time (up to a few sec) after the ATP binding. Biological studies have partially clarified the genetic and kinetic regulation of the rotation in MF1. Both theories (6, 7, 62, 64, 85) and the biological significance (17) of the intramolecular rotation of F0F1 await further studies, especially those of F0 and minor subunits.