Theoretical and partially experimental aspects of explosive crystallisation of glasses are reviewed. Quantitative criteria are formulated for thermal bistability of quasisteady crystallisation of glasses and for the absence of explosive crystallisation. Theoretical results are discussed for the critical parameters and the velocity of an explosive crystallisation front allowing for the heat transfer conditions and for the geometry of the crystallisation front. A classification of glasses is proposed on the basis of their stability against explosive crystallisation of metallic, semiconducting, and insulating glasses. The peculiarities of explosive front propagation in partially crystallised glasses are also discussed. It is shown that there is a satisfactory qualitative and quantitative agreement between the theory and experiment.