This paper analyses the methods and technologies involved in flapping-wing flying robots (FWFRs), where the actuation of the flapping wing produces thrust and lift force that mimics birds’ and insects’ flight. The focus is on the evolution of the flapping-wing technology and the challenges in prototyping, modeling, navigation, and control. The mechanism for flapping production, frequency control of the flapping, and wing/tail control for positioning the robot are important topics for successful prototyping. The article includes the study of the dynamics and aerodynamics of the FWFR. Using the combination of flapping and gliding has led researchers to seek more energy savings through this hybrid-in-nature dynamic system, which benefits from the wind, a natural and free energy source. The paper reviews the dynamics, design, and categorization of flapping-wing systems; it also includes control and onboard intelligent functionalities, particularly environment perception for positioning and guidance, as well as obstacle detection and avoidance.