The problems of spin polarization of low-energy electrons interacting with solid surfaces are reviewed. Special attention is paid to describing the methodology of obtaining beams of polarized electrons, methods of analyzing the spin state of the electrons in a beam, and also to the method of spin-polarized low-energy electron diffraction. Results are presented of theoretical and experimental study of the energy, angular, and temperature-dependences of the spin polarization of electrons scattered by solid surfaces, and of the effect of adsorption on the polarization of electrons for nonmagnetic and magnetic surfaces. Experiments to study the spin polarization of inelastically scattered electrons are described. In conclusion the prospects of studies involving analysis of the spin state of emitted and scattered electrons are pointed out.