The ROBUR project aims at developing a series of capacities that are inspired from those of birds, bats or insects, and that might contribute to the autonomy of UAV. However, although the ultimate goal is to integrate these capacities in a single flapping-wing platform, several preliminary studies described in this paper concern more classical platforms like planes or helicopters. The capacities under study can be grouped in three different categories: flapping-wing flight, reflexes and high-level behaviours. Research efforts in the first category concern the understanding of the aerodynamics of flapping-wing flight, and aim at designing appropriate morphologies and controllers that may serve to implement the corresponding behaviour on a robotic platform. The second category concerns the implementation of some reflexes, like those of obstacle-avoidance or speed-regulation, likely to contribute to an UAV's safety in its environment. As for high-level behaviours, they cover a wider range of capacities. Their role is to turn the UAV from a mere teleoperated engine to a fully autonomous robot. This entails capacities like being able to spare its energy expenditures, to know its current localization, and to decide what to do at every moment. This article describes the major results already obtained within the framework of this project.