A vehicle may have a vehicle body and one or more movable sensors mounted to the body. A movable sensor may be rotated, linearly translated, or otherwise moved between multiple positions in response to location information, driving mode information, vehicle speed, and/or other information. The movable sensor may be moved to track objects, to provide pedestrians and others with visual feedback, to allow the sensor to gather desired sensor information to support driver assistance and autonomous driving operations, to place the sensor in a stowed position, and to perform other functions. The movable sensor may be protected with a movable cover. A cleaner may clean the sensor. The sensor may be a radar sensor, lidar sensor, camera, or other sensor. Information from the sensor may be used to detect roadway obstructions, to detect objects near the vehicle, to monitor pedestrians, and to monitor other conditions.