With the rapid development of society, global energy is in short supply. China has put forward an integrated energy system focusing on interconnecting energy resources and harnessing their complementary advantages to address the energy crisis, thus no longer pursuing the production, transportation and supply of a single source of energy. In the continuous development of integrated energy systems, the elements of participation and interaction are becoming more complex. Game theory, which can effectively solve the problems arising from multi-agent trading, is naturally introduced to the integrated energy system. This paper provides a comprehensive overview of the introduction of game theory into the integrated energy system. First, the development of integrated energy is briefly introduced, game scenarios in integrated energy systems is proposed, and game scenarios considering the energy supply side, distribution network, demand side and common planning and dispatching problems in integrated energy systems are summarized. Secondly, main game theory models in the integrated energy system are summarized, such as cooperative game theory model, the non-cooperative game theory model and the Stackelberg game theory model. Finally, the future prospect and challenge for the application of game theory in integrated energy systems is proposed. The new game models are introduced to the integrated energy system, and a mixed game is considered to solve related problems. It is hoped that this work can serve as a reference for the researchers in this field. INDEX TERMS Integrated energy system, game theory, energy management, demand response.