The laser-induced relativistic shock waves are described. The shock waves can be created directly by a high irradiance laser or indirectly by a laser acceleration of a foil that collides with a second static foil. A special case of interest is the creation of laser-induced fusion where the created alpha particles create a detonation wave. A novel application is suggested with the shock wave or the detonation wave to ignite a pre-compressed target. In particular, the deuterium–tritium fusion is considered. It is suggested that the collision of two laser accelerated foils might serve as a novel relativistic accelerator for bulk material collisions.