The shape and function of insect wings tremendously vary between insect species. This review is engaged in how wing design determines the aerodynamic mechanisms with which wings produce an air momentum for body weight support and flight control. We work out the tradeoffs associated with aerodynamic key parameters such as vortex development and lift production, and link the various components of wing structure to flight power requirements and propulsion efficiency. A comparison between rectangular, ideal-shaped and natural-shaped wings shows the benefits and detriments of various wing shapes for gliding and flapping flight. The review expands on the function of three-dimensional wing structure, on the specific role of wing corrugation for vortex trapping and lift enhancement, and on the aerodynamic significance of wing flexibility for flight and body posture control. The presented comparison is mainly concerned with wings of flies because these animals serve as model systems for both sensorimotor integration and aerial propulsion in several areas of biology and engineering.