Micro air vehicles (MAVs) with a wingspan of or shorter, and flight speed around have attracted substantial interest in recent years. There are several prominent features of MAV flight: (i) low Reynolds number , resulting in degraded aerodynamic performance, (ii) small physical dimensions, resulting in certain favorable scaling characteristics including structural strength, reduced stall speed, and impact tolerance, and (iii) low flight speed, resulting in order one effect of the flight environment and intrinsically unsteady flight characteristics. Flexible wings utilizing membrane materials are employed by natural flyers such as bats and insects. Compared to a rigid wing, a membrane wing can better adapt to the stall and has the potential for morphing to achieve enhanced agility and storage consideration. We will discuss the aerodynamics of both rigid and membrane wings under the MAV flight condition. To understand membrane wing performance, the fluid and structure interaction is of critical importance. Flow structures associated with the low Reynolds number and low aspect ratio wing, such as pressure distribution, separation bubble, and tip vortex, as well as structural dynamics in response to the surrounding flow field are discussed. Based on the computational capabilities for treating moving boundary problems, an automated wing shape optimization technique is also developed. Salient features of the flexible-wing-based MAV, including the vehicle concept, flexible wing design, novel fabrication methods, aerodynamic assessment, and flight data analysis are highlighted.