Abstract: The research progress and development status of studies on oblique detonation waves in supersonic flows are summarized. Experimental investigations on the initiation and stability of oblique detonation waves are firstly provided, especially on the initiation criterion and the formation condition of different transition structures. Then studies on the transition structure and the cellular structure are reviewed, where the effects of the inflow condition and the wedge angle on the wave structures are introduced. Besides, studies on the interaction between the oblique detonation wave and the turbulence boundary layer are reviewed. Some challenges in current studies are analyzed and some suggestions on future studies on oblique detonation waves are given.