Aerial swarms have the potential to search for forest fires, chemical plumes or victims and serve as communication and sensor networks in the sky. Flying robots are interesting for such applications because they are fast, can easily overcome difficult terrain and provide line-of-sight communication or aerial perspectives. However, swarms of flying robots have so far only been demonstrated in simulation or in few examples in reality. Current simulators typically rely on unrealistic assumptions concerning robot sensing capabilities and motion. To bridge this reality gap we propose to address two key challenges. The first challenge consists in discovering swarm controllers that do not use position information. Swarm controllers in the literature rely on global or relative position information which can be obtained using GPS, cameras or range and bearing sensors. However, position requirements typically entail robots that are complex, heavy and expensive or that rely on specific environmental conditions to function. Lifting the need for position could instead lead to swarm controllers that can be deployed in a variety of environments and using very simple robots. The second challenge addressed consists in developing swarm controllers that can accommodate motion constraints of flying robots. In particular, we consider fixed-wing robots that can not stop or turn on the spot like ground robots or rotor crafts. Instead they must fly at relatively high speeds to avoid stalling. Therefore, making the robots advance slowly in average can only be done by having them turn. To address these challenges, we consider robot controllers that continuously react to wireless communication with neighboring robots or people by changing their turn rate (communication-based behaviors). Using communication as a sensor for flying robots is interesting because most robots are equipped with off-the-shelf radio modules that are low-cost, light-weight and relatively long-range. The design of robot controllers that can lead to desired swarm behaviors is done following a systematic approach. First, artificial evolution is used to automatically discover simple and unthought-of controllers for swarms of flying robots. Evolved controllers are then reverse engineered to obtain basic behaviors that can be modeled and used in a variety of swarm applications. In order to discover a range of basic behaviors, we consider a challenging swarm application that requires robots to direct themselves in their environment, move in groups, cover an area, and maintain a communication relay. Discovered behaviors are then extended to scenarios with wind. Overall, this thesis presents the evolutionary synthesis of communication-based behaviors for swarms of fixed-wing flying robots.