The construction of overlays is a crucial problem in the research of mobile peer-to-peer networks. The architecture of overlays determines the robustness, security and performance of MP2P networks. The paper first introduces the concept of mobile P2P overlays, including the definition, significance of the construction of overlays and the classification of them. Next, three kinds of overlays, distributed unstructured, distributed structured and semi distributed (hybrid) network, are described. The application of overlays in MANET, VANET and WMN is especially introduced. Furthermore, the aforementioned overlays are analyzed and compared. Finally, the paper concludes and presents the future research directions.