Mathematical modeling of radiation defects in crystals is currently one of the fundamental methods of theoretical study of radiation damage. This review gives the fundamental results obtained in this field in the 15 years that have elapsed since the appearance of the pioneering study of Vineyard. The results are discussed of studying the structure of low- and high-energy cascades, the role of thermal lattice vibrations, the interaction of focusons and crowdions with lattice defects, the equlibrium structure of radiation defects, post-cascade distributions of radiation defects, and their influence on the mechanical properties of solids.