The understanding of charged particle orbital dynamics in an electromagnetic field is necessary for the acceleration and the storage of particles. The understanding of spin (or magnetic moment) dynamics is essential for the acceleration and the storage of polarized particle beams. In this paper we review the analysis of the dynamics of the spin and the various schemes and devices up‐to‐date to manipulate the spin to conserve the polarization while accelerating and storing a polarized beam. We shall concentrate on hadrons such as protons, antiprotons and heavier ions although most of the discussions apply equally well to leptons. Electron and positron beams are self‐polarizing through spin‐flip synchrotron radiation at high energies and hence the acceleration of polarized e± beams is less relevant. (AIP)