Motivated by recent interest in developing flapping wing micro-air vehicles (MAVs) capable of emulating the flight performance of insects, we describe the state of the art in our understanding of insect flight dynamics. We first outline some general principles of flapping flight dynamics, before presenting a framework for modelling insect flight dynamics using empirical data from real insects. Using wind tunnel and rotary balance measurements to measure time-invariant stability/control derivatives and their time-periodic equivalents, we formulate linear time-invariant (LTI) and nonlinear time-periodic (NLTP) equations of motion describing the longitudinal flight dynamics of desert locusts. We use these models to formulate a practical definition of stability in flapping flight and discuss consequences for flapping flight control in terms of limit cycle control and periodic gain scheduling. We conclude by considering possible implications for flapping wing MAV design.