There are not yet fully autonomous flying robots capable of maneuvering in small cluttered environments as insects do. The substantial weight and energy constraints typically encountered in this kind of robotic applications preclude the use of powerful processors and classical distance sensors. Moreover, due to their highly dynamic motion, flying systems require fast sensory-motor mapping. To pave the way toward fully autonomous indoor flying robots we take inspiration from flying insects like flies because (i) they generally display efficient flight control capability in complex environments in spite of their limited weight and tiny brain, (ii) the sensory modalities they are using for flight control have artificial counterparts (sensors) that fit the limited available payload, and (iii) a large body of literature has been produced by biologists on their anatomy, sensors, processing pathways, and behaviors. The latest prototype we built is named MC1 and has an overall weight of 10 g including visual, inertial, and airflow sensors. It is capable of automatic take-off, speed regulation, and obstacle avoidance in a 7x6-m room equipped with randomly textured walls. To avoid collisions, it computes optic-flow from its onboard CMOS camera and fuses it with rotation rate information provided by a MEMS gyroscope. It has already demonstrated robust operation during several test flights, which lasted up to 10 minutes of autonomous operation.