Approximately 20 years have passed since the first isolation of tubulin, dynein and non-muscle actomyosin. During this period actomyosin, microtubule-dynein or microtubules plus other ATPases (kinesin) have been implicated in almost all cellular motile phenomena. A possible exception is that polymerization of actin in a preferred direction could be responsible for extending the leading edge of a fibroblast. We now tend to look for an explanation of a motile process in terms of the cross-bridge cycle or some variation on this general mechanism. It will be of considerable interest to determine whether the new system for organelle movement fits this concept. In spite of great progress in identifying the basis of motility, fundamental problems remain unsolved. The nature of the conformation change of actomyosin in the cross-bridge cycle is still unknown and the solution of this problem may require the determination of the three-dimensional structure of the actin-myosin-nucleotide complex. We are still at the stage of classifying proteins that bind to actin and microtubules. The control of the dynamic state of actin and the microtubules in the cell is still poorly understood. Recent studies give hope that it will be possible to understand the mechanism of mitosis, but the biochemical study of this problem has only just begun.