Recent progress on understanding fundamental mechanisms governing the Self-propagating High-temperature Synthesis (SHS) process, which is characterized by the flame propagation through a matrix of compacted reactive particles and is recognized to hold the practical significance in producing novel solid materials, is reviewed. Here the focus is not only on the theoretical description of the heterogeneous nature in the combustion wave, which has not been captured by the conventional premixed-flame theory for a homogeneous medium, but also on the extensive comparisons between the predicted and experimental results in the literature. Topics included are the statistical counting procedure used for deriving governing equations of the heterogeneous theory, flame propagation in the adiabatic condition, flame propagation and extinction under heat loss conditions, effects of bimodal particle dispersion on the combustion behavior, those of external heating by electric current, the transition boundary from steady to pulsating combustion, and the initiation of the combustion wave by use of the external heating source. The importance of heterogeneity in the combustion wave, that is the particle size of the nonmetal or the higher melting-point metal, has been emphasized for fundamental understanding of such combustion behavior as flame propagation, extinction, and initiation. Potentially promising research topics are also suggested.