Dragonfly wings possess great stability and high load-bearing capacity during flapping flight, glide, and hover. Scientists have been intrigued by them and have carried out research for biomimetic applications. Relative to the large number of works on its flight aerodynamics, few researchers have focused on the insect wing structure and its mechanical properties. The wings of dragonflies are mainly composed of veins and membranes, a typical nanocomposite material. The veins and membranes have a complex design within the wing that give rise to whole-wing characteristics which result in dragonflies being supremely versatile, maneuverable fliers. The wing structure, especially corrugation, on dragonflies is believed to enhance aerodynamic performance. The mechanical properties of dragonfly wings need to be understood in order to perform simulated models. This paper focuses on the effects of structure, mechanical properties, and morphology of dragonfly wings on their flyability, followed by the implications in fabrication and modeling.