Micro aerial vehicles using flapping wings are under investigation, as an alternative to fixed-wing and rotary-wing micro aerial vehicles. Such flapping-wing vehicles promise key potential advantages of high thrust, agility, and maneuverability, and have a wide range of applications. These applications include both military and commercial domains such as communication relay, search and rescue, visual reconnaissance, and field search. With the advancement in the computational sciences, developments in flapping-wing micro aerial vehicles have progressed exponentially. Such developments require a careful aerodynamic and aeroelastic design of the flapping wing. Therefore, aerodynamic tools are required to study such designs and configurations. In this paper, the role of several parameters is investigated, including the types of flapping wings, the effect of the kinematics and wing geometry (shape, configuration, and structural flexibility) on performance variables such as lift, drag, thrust, and efficiency in various modes of flight. Kinematic variables have a significant effect on the performance of the flapping wing. For instance, a high flap amplitude and pitch rotation, which supports the generation of the strong leading-edge vortex, generates higher thrust. Likewise, wing shape, configuration, and structural flexibility are shown to have a large impact on the performance of the flapping wing. The wing with optimum flexibility maximizes thrust where highly flexible wings lead to performance degradation due to change in the effective angle of attack. This study shows that the development of the flexible flapping wing with performance capabilities similar to those of natural fliers has not yet been achieved. Finally, opportunities for additional research in this field are recommended.