Abstract: Hover-capable flapping-wing micro air vehicles (FWMAVs), inspired by insects or hummingbirds, exhibit remarkable flight characteristics such as hovering capability, high aerodynamic efficiency at low Reynolds numbers, and strong stealthiness, offering diverse potential applications in disaster rescue, emergency response, and environmental monitoring. However, the aerodynamic forces and efficiency of their flapping wings still lag considerably behind those of their biological counterparts, adversely affecting the endurance and payload capacity of FWMAVs and significantly limiting their practical applications. This paper provides a comprehensive overview of hover-capable FWMAVs, with a focus on current research progress, theoretical and experimental methods for aerodynamic analysis, the high-lift mechanisms of insects and their applications in FWMAVs, as well as aerodynamic design methods and performance evaluation of flapping wings. The review highlights key design parameters for achieving high lift, high aerodynamic efficiency, and low noise, and elucidates the impact of these parameters on the performance of FWMAVs. Finally, future trends in aerodynamic design for hover-capable FWMAVs are discussed, offering valuable guidance for future research in this field.