The synthesis of advanced materials by a wave of heterogeneous combustion propagating through a charge mixture, or the so-called self-propogating high-temperature synthesis (SHS) has many potential advantages over conventional techniques of synthesis. Because of high heating rates, steep temperature and concentration gradients, and fast accomplishment of reactions, the mechanisms of physical, chemical and structural transformations in the SHS wave are intricate and often not known. Further understanding of interaction mechanisms in SHS waves, relating the process parameters to structure and properties of the target material, and the application of SHS to producing final articles necessitates developing mathematical models for SHS-related phenomena. Various aspects of mathematical modelling of SHS are discussed in this paper. They include the analysis of novel factors influencing the structure formation, viz. the heating-to-reaction and mass transfer-to-reaction time ratios, autocatalysis and intrinsic stochasticity, which are unnoticed in traditional synthesis methods. The application of chemical thermodynamics and combustion theory to modelling SHS processes is outlined. Novel mathematical models are developed for SHS on condensed systems, which involve stochastic effects and autocatalysis. New models for solid-gas systems are worked out, which include the reaction kinetics and mass transfer of a gaseous reactant and permit predicting the structure formation pattern in the SHS wave. Application of mathematical modelling to producing porous final articles by means of SHS is discussed.