The combustion synthesis (CS) of materials is an advanced approach in powder metallurgy. The number of products synthesized by CS has increased rapidly during recent years and currently exceeds 1,000 different compounds. The same features, such as high temperatures and rates, self-sustained manner of microstructure formation in non-equilibrium conditions, that make CS an attractive technology also define difficulties to study the nature and mechanisms of this process, which in turn are essential to control the properties of the synthesized materials. In this survey paper, we present results of our recent work both in fundamental studies of mechanisms for rapid reaction wave propagation in heterogeneous media and in using the CS approach to synthesize different types of advanced materials, including bio-alloys and nano-sized powders.