A systematic review is given of the phenomenon of spin polarization in electronic and atomic collisions, which has recently been the subject of experimental investigation. These experiments are topical and important because polarization phenomena are associated with interference and thus constitute a very precise and sensitive means of investigating the structure and properties of matter and of analyzing physicochemical processes. A unified theory of polarization phenomena in electronic and atomic collisions, which includes an account of the most recent known experiments, is presented. The unified description is achieved with the aid of the scattering amplitude matrix and the spin density matrix formalism. Particular attention is devoted to processes in two-particle systems consisting of particles with spins 1/2 and 1. Processes involving a change in the spin of the target, which occurs as a result of exchange interactions, are characteristic for electron-atomic collisions. Exchange excitation of atoms and Penning ionization processes are examples of such collisions. The theory of polarization produced in such processes is reviewed and whenever possible, the results are compared with experimental data. Possible future applications of polarized electrons in the physics of electronic and atomic collisions are indicated.