We address the problem of high speed autonomous navigation of quadrotor micro aerial vehicles with limited onboard sensing and computation. In particular, we propose a dual range planning horizon method to safely and quickly navigate quadrotors to specified goal locations in previously unknown and unstructured environments. In each planning epoch, a short-range planner uses a local map to generate a new trajectory. At the same time, a safe stopping policy is found. This allows the robot to come to an emergency halt when necessary. Our algorithm guarantees collision avoidance and demonstrates important advances in real-time planning. First, our novel short range planning method allows us to generate and re-plan trajectories that are dynamically feasible, comply with state and input constraints, and avoid obstacles in real-time. Further, previous planning algorithms abstract away the obstacle detection problem by assuming the instantaneous availability of geometric information about the environment. In contrast, our method addresses the challenge of using the raw sensor data to form a map and navigate in real-time. Finally, in addition to simulation examples, we provide physical experiments that demonstrate the entire algorithmic pipeline from obstacle detection to trajectory execution.