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Performing acrobatic maneuvers with quadrotors is extremely challenging. Acrobatic flight requires high thrust and extreme angular accelerations that push the platform to its physical limits. Professional drone pilots often measure their level of mastery by flying such maneuvers in competitions. In this paper, we propose to learn a sensorimotor policy that enables an autonomous quadrotor to fly extreme acrobatic maneuvers with only onboard sensing and computation. We train the policy entirely in simulation by leveraging demonstrations from an optimal controller that has access to privileged information. We use appropriate abstractions of the visual input to enable transfer to a real quadrotor. We show that the resulting policy can be directly deployed in the physical world without any fine-tuning on real data. Our methodology has several favorable properties: it does not require a human expert to provide demonstrations, it cannot harm the physical system during training, and it can be used to learn maneuvers that are challenging even for the best human pilots. Our approach enables a physical quadrotor to fly maneuvers such as the Power Loop, the Barrel Roll, and the Matty Flip, during which it incurs accelerations of up to 3g.