In recent years, there has been rapid advancement in the application of artificial intelligence technology to sequential decision-making and adversarial game scenarios, resulting in significant progress in domains such as Go, games, poker, and Mahjong. Notably, systems like AlphaGo, OpenAI Five, AlphaStar, DeepStack, Libratus, Pluribus, and Suphx have achieved or surpassed human expert-level performance in these areas. While these applications primarily focus on zero-sum games involving two players, two teams, or multiple players, there has been limited substantive progress in addressing mixed-motive games. Unlike zero-sum games, mixed-motive games necessitate comprehensive consideration of individual returns, collective returns, and equilibrium. These games are extensively applied in real-world applications such as public resource allocation, task scheduling, and autonomous driving, making research in this area crucial. This study offers a comprehensive overview of key concepts and relevant research in the field of mixed-motive games, providingan in-depth analysis of current trends and future directions both domestically and internationally. Specifically, this study first introduces the definition and classification of mixed-motive games. It then elaborates on game solution concepts and objectives, including Nash equilibrium, correlated equilibrium, and Pareto optimality, as well as objectives related to maximizing individual and collective gains, while considering fairness. Furthermore, the study engages in a thorough exploration and analysis of game theory methods, reinforcement learning methods, and their combination based on different solution objectives. In addition, the study discusses relevant application scenarios and experimental simulation environments before concluding with a summary and outlook on future research directions.