Automatic landing on extraterrestrial bodies is still a challenging and hazardous task. Here we propose a new type of autopilot designed to solve landing problems, which is based on neurophysiological, behavioral, and biorobotic findings on flying insects. Flying insects excel in optic flow sensing techniques and cope with highly parallel data at a low energy and computational cost using lightweight dedicated motion processing circuits. In the first part of this paper, we present our biomimetic approach in the context of a lunar landing scenario, assuming a 2-degree-of-freedom spacecraft approaching the moon, which is simulated with the PANGU software. The autopilot we propose relies only on optic flow (OF) and inertial measurements, and aims at regulating the OF generated during the landing approach, by means of a feedback control system whose sensor is an OF sensor. We put forward an estimation method based on a two-sensor setup to accurately estimate the orientation of the lander's velocity vector, which is mandatory to control the lander's pitch in a near optimal way with respect to the fuel consumption. In the second part, we present a lightweight Visual Motion Sensor (VMS) which draws on the results of neurophysiological studies on the insect visual system. The VMS was able to perform local 1-D angular speed measurements in the range 1.5°/s - 25°/s. The sensor was mounted on an 80 kg unmanned helicopter and test-flown outdoors over various fields. The OF measured onboard was shown to match the ground-truth optic flow despite the dramatic disturbances and vibrations experienced by the sensor.