Research made over the past decade shows the use of increasingly complex methods and heavy platforms to achieve autonomous flight in cluttered environments. However, efficient behaviors can be found in nature where limited sensing is used, such as in insects progressing toward a light at night. Interestingly, their success is based on their ability to recover from the numerous collisions happening along their imperfect flight path. The goal of the AirBurr project is to take inspiration from these insects and develop a new class of flying robots that can recover from collisions and even exploit them. Such robots are designed to be robust to crashes and can take-off again without human intervention. They navigate in a reactive way, bump into obstacles, and unlike conventional approaches, they don't need heavy modeling in order to fly autonomously. We believe that this new paradigm will bring flying robots out of the laboratory and allow them to tackle unstructured, cluttered environments. This paper aims at presenting the vision of the AirBurr project, as well as the latest results in the design of a platform capable of sustaining collisions and self-recovering after crashes.