Kinesin-1 is a single-molecule walking machine, driven by ATP turnover. Recent optical trapping experiments show that pulling backwards on a walking kinesin-1 molecule causes the mechanical walking action to reverse, while the coupled chemical cycle of ATP turnover continues, apparently, to run forwards - kinesin can moonwalk. Individual forward- and back-steps are fast, and each appears to be a single event, complete in a few tens of microseconds, with no substeps. Between steps, kinesin pauses, waiting for the next ATP to arrive. Several lines of evidence indicate that during these between-step dwells, only one of the two heads is strongly attached to the microtubule. The position of the other head during the dwells is less certain, and more controversial.