The flight of a thin wing or plate is an archetypal problem in flow-structure interactions at intermediate Reynolds numbers. Free-falling plates display an impressive variety of steady and unsteady motions that are familiar from fluttering leaves, tumbling seeds and gliding paper planes, while flapping wings or foils are emblematic of bird flight and fish swimming. This talk will show that the key behaviors of both passive and flapping flight may be captured by a quasi-steady nonlinear aerodynamic model that predicts forces from plate kinematics without needing to solve for the flows. Regarding passive flight, we show that this nonlinear model successfully reproduces previously documented unsteady states such as fluttering and tumbling while also predicting new types of motions, and a linear analysis accurately accounts for the stability of steady states such as gliding and diving. Regarding flapping flight, simulations reproduce the well-known transition for increasing Reynolds number from a stationary state to a propulsive state, where the latter is characterized by a Strouhal number that is conserved across broad ranges of parameters. These findings extend the phenomena of unsteady locomotion that can be explained by quasi-steady modeling, and they broaden the conditions and parameter ranges over which such models are applicable.