Self-propagating high-temperature synthesis (SHS), also known as combustion synthesis, is one of the most prospective methods for production functionally graded materials (FGM). The advantages of SHS include short time of reaction and product formation, which allow retaining pre-determined concentration gradient in the synthesized material. In the present work, the following challenges remaining in the field of FGM production by SHS are discussed. First, main features of combustion of multilayer samples are considered from the viewpoint of mutual influence of the combustible and inert layers. Second, evolution of the concentration gradients (profiles) during the combustion is outlined and different methods for controlling this process, such as mechanical pre-activation of the reactants are examined. Third, processes of the product phase and microstructure formation in multilayer SHSmaterials are described. The problem of creating very thin gradient samples and coatings by SHS is also discussed. The consideration includes data of high-speed video recording, timeresolved X-ray diffraction, SEM, EPMA and other experimental techniques.