For large unmanned aerial vehicle (UAV) networks, the timely communication is needed to accomplish a series of missions accurately and effectively. The relay technology will play an important role in UAV networks by helping drones communicating with long-distance drones, which solves the problem of the limited transmission power of drones. In this paper, the relay selection is seen as the entry point to improve the performance of self-organizing network with multiple optimizing factors. Different from the ground relay models, the relay selection in UAV communication networks presents new challenges, including heterogeneous, dynamic, dense and limited information characteristics. More effective schemes with distributed, fast, robust and scalable features are required to solve the optimizing problem. After discussing the challenges and requirements, we find that the matching game is suitable to model the complex relay model. The advantages of the matching game in selforganizing UAV communications are discussed. Moreover, we provide extensive applications of matching markets, and then propose a novel classification of matching game which focuses on the competitive relationship between players. Specifically, basic preliminary models are presented and some future research directions of matching game in UAV relay models are discussed. ). due to the limited transmission capacity, the heavy UAVto-infrastructure communication hardware and the unreliable communication [3], it is difficult for all UAVs to connect with the satellite. With large-scale deployment and intensive cooperation of UAVs, it is meaningful to discuss the internal communication [4] of UAVs. In more extreme cases, if satellite communications are disrupted, effective internal communications can guarantee the completion of the mission.In the internal communication, the technology of short haul communication is used. As shown in Fig. 1, due to the complexity of the spatial distribution, the UAV network needs to be divided into several coalitions to finish the comprehensive missions. Within the network, the internal communication of UAVs involves the control information exchange and the service information fusion. The information sharing mainly implements the information interaction among coalitions of UAVs, so as to configure the UAV coalitions and assign tasks. The information fusion mainly refers to the information exchange between the units within the UAVs, so drones can assess the overall situation and accomplish tasks.Because of the transmission power constraint of drones, it is difficult to achieve reliable communications among the whole UAV network. Some drones should be used as relay devices to improve the quality of the communication. However, the large scale of UAVs, the self-organization of UAV coalition and the intensive external interference make the relay selection of UAV communication more difficult. Considering the complexity of the UAV communication, this article mainly provides a new perspective of developing distributed and robust relay s...