Theoretical and partially experimental aspects of explosive crystallization of glasses are reviewed. Quantitative criteria are formulated for thermal bistability of quasisteady crystallization of glasses and for the absence of explosive cystallization. Theoretical results are discussed for the critical parameters and the velocity of an explosive crystalliztion front allowing for the heat transfer conditions and for the geometry of the crystallization front (which may be plane, circular, or spherical). A classification of glasses is proposed on the basis of their stability against explosive crystallization and a quantiative analysis is made of the putlished experimental data on explosive crystallization of metallic, semiconducting, and insulating glasses.