Abstract: With the commercial process of the fifth generation (5G) mobile communication system, device-to-device (D2D) communication is attracting researchers' attention. As the key technology of optimizing D2D communication, resource allocation has become an important research topic, such as frequency and power. In this survey, the D2D resource allocation in cellular networks was revised in this paper. First, the D2D communication model and mode were introduced. Then, the main methods of D2D communication resource allocation in cellular networks were analyzed from the perspective of different mathematical theories. The theories include graph theory, hypergraph theory, game theory, machine learning, heuristic algorithm, and so on. Furthermore, the advantages and disadvantages of these algorithms were compared. Finally, the open issues of D2D resource allocation method and the future research directions of D2D communication in cellular networks were prospected.