Autonomous navigation in unknown environments with obstacles remains challenging for micro aerial vehicles (MAVs) due to their limited onboard computing and sensing resources. Although various collision avoidance methods have been developed, it is still possible for drones to collide with unobserved obstacles due to unpredictable disturbances, sensor limitations, and control uncertainty. Instead of completely avoiding collisions, this article proposes Air Bumper, a collision detection and reaction framework, for fully autonomous flight in 3D environments to improve the safety of drones. Our framework only utilizes the onboard inertial measurement unit (IMU) to detect and estimate collisions. We further design a collision recovery control for rapid recovery and collision-aware mapping to integrate collision information into general LiDAR-based sensing and planning frameworks. Our simulation and experimental results show that the quadrotor can rapidly detect, estimate, and recover from collisions with obstacles in 3D space and continue the flight smoothly with the help of the collision-aware map.