The design of micro aerial vehicles has been long inspired by biological flyers such as birds and insects. The aerodynamic principles of flapping wing flights are complex due to the rapid wing motion and the inherent complex vortex dynamics. Several experimental and numerical investigations have been carried out in the past decades to uncover the mechanisms responsible for the improved aerodynamic capability of flapping wings. This paper provides an overview of the aerodynamics of flapping insect wings. After providing a brief overview of the aerodynamics of a single wing, we discuss how the vortex dynamics are altered in the case of tandem wings. A significant challenge to designing a stable MAV is the environmental effects stemming from the gust and ground presence. In this paper, we present how the force generation is altered due to such effects. Moreover, we point out unsolved research questions on insect flight whose answers could greatly help to improve the design of flapping wing MAVs.