Aerodynamic forces render accurate high-speed trajectory tracking with quadrotors extremely challenging. These complex aerodynamic effects become a significant disturbance at high speeds, introducing large positional tracking errors, and are extremely difficult to model. To fly at high speeds, feedback control must be able to account for these aerodynamic effects in real-time. This necessitates a modeling procedure that is both accurate and efficient to evaluate. Therefore, we present an approach to model aerodynamic effects using Gaussian Processes, which we incorporate into a Model Predictive Controller to achieve efficient and precise real-time feedback control, leading to up to 70% reduction in trajectory tracking error at high speeds. We verify our method by extensive comparison to a state-of-theart linear drag model in synthetic and real-world experiments at speeds of up to 14m/s and accelerations beyond 4g. SUPPLEMENTARY MATERIALVideo: https://youtu.be/FHvDghUUQtc Code: https://github.com/uzh-rpg/data driven mpc I. INTRODUCTIONAccurate trajectory tracking with quadrotors in high-speed and high-acceleration regimes is still a challenging research problem. While autonomous quadrotors have seen a significant gain in popularity and have been applied in a variety of industries ranging from agriculture to transport, security, infrastructure, entertainment, and search and rescue, they still do not exploit their full maneuverability. The ability to precisely control drones during fast and highly agile maneuvers would allow to not only fly fast in known-free environments, but also close to obstacles, humans, or through openings, where already small deviations from the reference have catastrophic consequences.Operating a quadrotor at high speeds and controlling it through agile, high-acceleration maneuvers requires to account for complex aerodynamic effects acting on the platform. These effects are difficult to model, since they consist of a combination of propeller lift and drag dependent on the induced airstream velocity, fuselage drag, and complex or even turbulent effects due to the interaction between the propellers, the downwash of other propellers, and the fuselage.