In this article we reviewed the main concepts of detonative combustion. Concepts of slow and fast combustion, of detonation adiabat are introduced. Landmark works on experimental and semi-empirical detonation study are presented. We reviewed Chapman-Jouguet stationary detonation and spin detonation. Various mathematical model of detonation wave have been reviewed as well. Works describing study of the instability and complex structure of the detonation wave front are presented. Numerical methods, results of parametric and asymptotic analysis of detonation propagation in channels of various forms are reviewed. It is shown that initiation of detonation is the main problem. Its various possible forms have been discussed. Laser ignition of fuel-air mixture was discussed separately and potential advantages of such initiation were demonstrated.