Abstract: Detonation cycle is an isochoric Fickett-Jacobs thermodynamic cycle, while the deflagration cycle is an isobaric Brayton-Joule one. The thermodynamic efficiency of Fickett-Jacobs cycle is higher than that of the Brayton-Joule, which is a main motivator for the applications of detonative combustion to the supersonic propulsion system. This paper summarized the results of theory and progress for detonation propulsion in supersonic flow, and analyzed the remaining scientific and technological problems, providing a guidance for the future investigations on hypersonic engines. The development of oblique detonation engine (ODE) and supersonic pulsed detonation ramjet engine (SPDRE) was reviewed. For the ODE, the application modes of ODE, the methods of experimental investigation, and the development of numerical studies were summarized. For the SPDRE, the current status and difficulties were reviewed. The detonation driven scramjet engines are advantageous for the self-pressurization, high combustion efficiency, high thrust performance, high propulsive efficiency, short chamber length, and light weight. The development and current progress were summarized, and the future development direction and technical problems were analyzed.