Many drone platforms have matured to become nearly optimal flying machines with only modest improvements in efficiency possible. “Chimera” craft combine fixed wing and rotary wing characteristics while being substantially less efficient than both. The increasing presence of chimeras suggests that their mix of vertical takeoff, hover, and more efficient cruise is invaluable to many end users. We discuss the opportunity for flapping wing drones inspired by large insects to perform these mixed missions. Dragonflies particularly are capable of efficiency in all modes of flight. We will explore the fundamental principles of dragonfly flight to allow for a comparison between proposed flapping wing technological solutions and a flapping wing organism. We chart one approach to achieving the next step in drone technology through systems theory and an appreciation of how biomimetics can be applied. New findings in dynamics of flapping, practical actuation technology, wing design, and flight control are presented and connected. We show that a theoretical understanding of flight systems and an appreciation of the detail of biological implementations may be key to achieving an outcome that matches the performance of natural systems. We assert that an optimal flapping wing drone, capable of efficiency in all modes of flight with high performance upon demand, might look somewhat like an abstract dragonfly.