Swarms of autonomous MAVs show great potential in many diverse applications. In a search and rescue mission, a group of MAVs could quickly reach disaster areas by flying over obstacles, cluttered and inaccessible terrains, and work in parallel to detect and locate people that are in need of help. However, multiple challenges still remain in the design of truly autonomous MAV teams. Due to the strict constraints imposed on the MAVs in terms of size, weight, 3D coverage, processing power, power consumption and price, there are not many technological possibilities that could provide individuals with information abut the position of themselves and their team mates without the aid of external systems. Inspired by the sense of hearing among many animal groups which use sound for localization purposes, we propose an on-board audio-based system for allowing individuals in an MAV swarm to use sound waves for obtaining the relative positioning, and furthermore, the self-localization information. We show that not only such a system fully satisfies the constraints of MAVs and is capable of obtaining these information, but also provides additional important opportunities, such as the detection and localization of crucial acoustic targets in the environment. Operating during night time, through foliage and in adverse weather conditions such as fog, dust and smoke, and detection and collision avoidance with non-cooperative noise-emitting aerial platforms are some of the potential advantages of audio-based swarming MAVs. In this thesis, we firstly describe an on-board sound-source localization system and novel methods for the innovative idea of localizing emergency sound sources on the ground from airborne MAVs. The ability of MAVs to locate source of distress sound signals, such as the sound of an emergency whistle blown by a person in need of help or the sound of a personal alarm, is significantly important and would allow fast localization of victims and rescuers during night time and in fog, dust, smoke and dense forests. We propose three different methods for overcoming the ambiguities related with localizing emergency sound sources or, in general, narrowband sound sources. Furthermore, we present the on-board audio-based relative positioning system for obtaining information about the position of other MAVs in their vicinity. We initially describe a passive method that exploits only the engine sound of other robots, in the absence of the self-engine noise, to measure their relative directions. We then extend this method to overcome some of its limitations, where individuals generate a chirping sound similar to the sound of birds to assist others in obtaining their positions. We then describe an estimator based on particle filters that fuses the relative bearing measurements with information about the motion of the robots, provided by their onboard sensors, to also obtain an estimate about the relative range of the robots. Finally, we present a cooperative method to address the self-localization problem for a team of MAVs, while accommodating the motion constraints of flying robots, where individuals obtain their three dimensional positions through perceiving a sound-emitting beacon MAV. All methods are based on coherence testing among signals of a small on-board microphone array, to measure the probable direction of incoming sound waves, and estimators for robust estimation of the desired information throughout time.