Self-propagating high-temperature synthesis (SHS) of powder compacts is a novel processing technique currently being developed as a route for the production of engineering ceramics and other advanced materials. The process, which is also referred to as combustion synthesis, provides energy- and cost-saving advantages over the more conventional processing routes for these materials. At the same time, the rapid heating and cooling rates provide a potential for the production of metastable materials with new and, perhaps, unique properties. This paper reviews the research that has been, and is being, undertaken in this exciting new processing route for high-technology materials and examines the underlying theoretical explanations which will, eventually, lead to improved control over processing parameters and product quality.