The application of the process of self-propagating high-temperature synthesis (SHS) to prepare highly dispersed powder nitride-carbide compositions from the most common refractory nitride (Si3N4, AlN, TiN) and carbide (SiC) compounds with a particle size of less than 1 μm is considered. The advantages of composite ceramics over single-phase ceramic materials and such trends of its development as the transition to nanostructured ceramics and the application of in situ processes of direct chemical synthesis of nanoparticles of components in the composite body are described. The attractiveness of the SHS process as one of the promising in situ processes characterized by simplicity and cost-effectiveness, the possibility of obtaining highly dispersed ceramic powders by burning mixtures of inexpensive reagents is shown. Considerable attention is paid to the consideration of the results of the application of azide SHS, based on the use of sodium azide and gasified halide salts as part of mixtures of initial powders of nitrided and carbidized elements during their combustion in nitrogen gas. The review of publications devoted to the application of SHS to obtain highly dispersed composite powders Si3N4–SiC, AlN–SiC and TiN–SiC, promising for use in sintering of the corresponding composite ceramic materials of submicron and nano-sized structure with improved properties, lower brittleness, good machinability, lower sintering temperatures compared with single-phase ceramic materials made of nitrides or carbides as well as for other applications, is presented. The results of the application of azide SHS are presented in detail both in the form of the results of thermodynamic calculations and the results of experimental research of combustion parameters, combustion product structure and composition. The advantages and disadvantages of using the combustion process for the synthesis of nitride compositions with silicon carbide, the causes of the disadvantages and the directions of further research to eliminate them are discussed.