We study the stability and control of flapping flight of insects. To quantify the stability and to assess the control, we build a 3D dynamic flight model, which takes into account the instantaneous coupling between the insect body and the wings. To compare with published results, we also implement a time-averaged model where aerodynamic forces are averaged over every wing-beat. To stabilize hovering flight, we design a control algorithm that incorporates a discrete sampling and a time delay within neural feedback circuits. Our study suggests conditions that the sampling interval and the delay time should satisfy so as to actively stabilize flapping flight. We also investigate how passive stability can be achieved for flapping flight by tuning wing attachment points. Finally, we extend our stability analysis and controller design to ascending flight.