In recent years there has been a considerable advance in understanding the spin motion of particles in storage rings and accelerators. The survey presented here outlines the early historical development in this field, describes the basic ideas governing the kinetics of polarized particles in electromagnetic fields and shows how these have evolved into the current description of polarized beam behaviour. Orbital motion of particles influences their spin precession, and depolarization of a beam can result from excitation of spin resonances by orbit errors and oscillations. Electrons and positrons are additionally influenced by the quantized character of synchrotron radiation, which not only provides a polarizing mechanism but also enhances depolarizing effects. Progress in the theoretical formulation of these phenomena has clarified the details of the physical processes and suggested improved methods of compensating spin resonances. Full use of polarized beams for high-energy physics with storage rings requires spin rotators to produce longitudinal polarization in the interaction regions. Variants of these schemes, dubbed Siberian snakes, provide a curious precession topology which can substantially reduce depolarization in the high-energy range. Efficient polarimetry is an essential requirement for implementing polarized beams, whose utility for physics can be enhanced by various methods of spin manipulation.