Insect-scale flapping wing flight vehicles can conduct environmental monitoring, disaster assessment, mapping, positioning and security in complex and challenging surroundings. To develop bio-inspired flight vehicles, systematic probing based on the particular category of flight vehicles is needed. This Element addresses the aerodynamics, aeroelasticity, geometry, stability and dynamics of flexible flapping wings in the insect flight regime. The authors highlight distinct features and issues, contrast aerodynamic stability between rigid and flexible wings, present the implications of the wing-aspect ratio, and use canonical models and dragonflies to elucidate scientific insight as well as technical capabilities of bio-inspired design.