Since the basic outline of the sliding filament mechanism became apparent some 45 years ago, the principal challenge, an experimental one, has been to produce definitive evidence about the detailed molecular mechanisms by which myosin cross–bridges produce force and movement in a muscle. More recently, similar questions could be posed about other molecular motors, in non–muscle cells. This problem proved unexpectedly difficult to solve, in part because of the technical difficulty of obtaining the structural and mechanical information required about rapid events within macromolecules, especially in a working system, and this triggered many remarkable technical developments. There is now very strong evidence for a large change in shape of the myosin heads during ATP hydrolysis, consistent with a leverarm mechanism. Whether this does indeed provide the driving force for contraction and movement— and, if so, exactly how—and whether some other processes could also play a significant role, is discussed in the light of the experimental and theoretical findings presented at this meeting, and other recent and long–term evidence.