Challenges for the controlled flight of a robotic insect are due to the inherent instability of the system, complex fluid-structure interactions, and the general lack of a complete system model. In this paper, we propose theoretical models of the system based on the limited information available from previous work and a comprehensive flight controller. The modular flight controller is derived from Lyapunov function candidates with proven stability over a large region of attraction. Moreover, it comprises adaptive components that are capable of coping with uncertainties in the system that arise from manufacturing imperfections. We have demonstrated that the proposed methods enable the robot to achieve sustained hovering flights with relatively small errors compared to a non-adaptive approach. Simple lateral maneuvers and vertical takeoff and landing flights are also shown to illustrate the fidelity of the flight controller. The analysis suggests that the adaptive scheme is crucial in order to achieve millimeter-scale precision in flight control as observed in natural insect flight.