Rocket based combined cycle (RBCC) engine is regarded as one of the most efficient propulsion systems for reusable space transportation vehicles and hypersonic cruise vehicles. It can perform excellently over a very broad range of Mach numbers and flight altitudes through multi-mode operations by effectively integrating high thrust-to-weight ratio of the rocket engine and high specific impulse of the airbreathing engine. The RBCC inlet, commonly operating in an extremely wide flight speed range covering static, subsonic, transonic, supersonic, and hypersonic, plays a vital role in the RBCC propulsion system and flight vehicles. This paper presents a comprehensive and systematical review of the research progress on the inlets for RBCC engines in different countries and different historical periods. A number of key technical and scientific issues specially concerning RBCC inlets are sorted out, including the wide range RBCC inlet design and optimization, inlet/embedded rocket/combustor matching and control, dynamic operation, etc. Several typical RBCC inlet applications and the corresponding research are discussed, including the Strutjet inlet, A5 inlet, GTX inlet, and the Astrox's inlet in the U.S., the RBCC inlet in JAXA, and a sidewall compression RBCC inlet in China. Finally, experience gained and some recommendations are summarized for future research of the RBCC inlet.