In recent years, with the rapid development of artificial intelligence technology in various sequential decision-making and adversarial game problems, remarkable progress has been made in the applications of Go, games, poker, and Mahjong. For example, systems of AlphaGo, OpenAI Five, AlphaStar, DeepStack, Libratus, Pluribus, and Suphx have achieved or surpassed human expert-level performance in these areas. These applications are focused on zero-sum games involving two players, two teams, or multiple players, while there is a lack of breakthrough or progress in the study of mixed-motive games. Distinguished from zero-sum games, mixed-motive games require comprehensive consideration of individual returns, collective returns, and equilibrium returns. They find extensive applications in real-world scenarios like public resource allocation, task scheduling, and autonomous driving. Therefore, research on mixed-motive games is crucial. This paper comprehensively reviews the crucial concepts and related work in the field of mixed-motive games and conducts an in-depth analysis of the current status and future development directions, both domestically and internationally. Specifically, this paper first introduces the definition and classification of mixed-motive games. Secondly, it elaborates on game solution concepts and objectives, including Nash equilibrium, correlated equilibrium, Pareto optimal, maximizing individual returns, maximizing collective returns, and considering fairness. Thirdly, it summarizes game theory methods, reinforcement learning methods, and combined methods according to different solution objectives. The paper also discusses relevant application scenarios and experimental simulation environments. Finally, the paper provides an outlook and summary of future research directions.