Unmanned aerial vehicles (UAVs) rely on optical sensors such as cameras and lidar for autonomous operation. However, such optical sensors are error-prone in bad lighting, inclement weather conditions including fog and smoke, and around textureless or transparent surfaces. In this paper, we ask: is it possible to fly UAVs without relying on optical sensors, i.e., can UAVs fly without seeing? We present BatMobility, a lightweight mmWave radar-only perception system for UAVs that eliminates the need for optical sensors. BatMobility enables two core functionalities for UAVs -- radio flow estimation (a novel FMCW radar-based alternative for optical flow based on surface-parallel doppler shift) and radar-based collision avoidance. We build BatMobility using commodity sensors and deploy it as a real-time system on a small off-the-shelf quadcopter running an unmodified flight controller. Our evaluation shows that BatMobility achieves comparable or better performance than commercial-grade optical sensors across a wide range of scenarios.