Bio-inspired Flapping-Wing Flying Robot (FWFR) mimicking the flight mechanism of animals like birds and insects in nature has the advantages of high safety and good disorientation, which has extremely significant application prospects in disaster rescue, antiriot and other aspects. In order to realize autonomous flight and perform detection tasks in unknown complex environments, a navigation system integrating functional modules such as perception and mapping, planning and obstacle avoidance, and flight control guidance, etc. need to be developed. This paper firstly gives an overview of the FWFR′s navigation system by classifying the robot into two categories of micro and medium-large according to the wingspan size, and then compares and analyzes the main research progresses in the navigation system of both FWFRs at home and abroad. Then, the key technologies involved in autonomous navigation systems such as perceptual localization and mapping, planning and obstacle avoidance, trajectory tracking and flight control guidance, etc. are analyzed and reviewed, the limitations and urgent problems are also pointed out. Finally, an outlook on future research trends is provided, including enhancing onboard embedded computing capabilities, multi-modal information fusion, multi-modal flight flow field perception, research of biomimetic vision systems, and swarm perception and formation control etc.