This review provides an analysis of the theoretical and experimental aspects of explosive crystallization of amorphous substances (glasses). Quantitative criteria are formulated for thermal bistability of quasisteady crystallization of glasses and for the absence of explosive crystallization. Expressions are derived for the critical parameters and the velocity of an explosive crystallization front allowing for the heat transfer conditions and for the geometry of the crystallization front (which may be plane, spherical, or circular). A systematic account is given of thermophysical characteristics and of the parameters governing the thermal stability of practically all the materials in which explosive crystallization has been discovered so far. Data on the velocity of propagation and temperature in an explosive crystallization front are also given. A classification of glasses is proposed on the basis of their stability against explosive crystallization and a quantitative analysis is made of the published experimental data on explosive crystallization of metallic, semiconducting, and insulating glasses. It is shown that there is a satisfactory qualitative and quantitative agreement between the theory and experiment.