This thesis presents the design and implementation of a small autonomous unmanned aerial vehicle capable of high-speed flight through complex natural environments. Using only onboard sensing and computation, we perform obstacle detection, planning, and feedback control in realtime. We introduce a novel stereo vision algorithm, pushbroom stereo, capable of detecting obstacles at 120 frames per second without overburdening our lightweight processors. Our use of model-based planning and control techniques allows us to track precise trajectories that avoid obstacles identified by the vision system. We demonstrate a complete working system avoiding trees at up to 14 m/s (31 MPH). To the best of our knowledge this is the fastest lightweight aerial vehicle to perform collision avoidance in such a complex environment.