<p>Recommender systems play a crucial role in mitigating information overload and have been extensively applied in domains such as e-commerce, news, and video-on-demand. A central challenge in their design is balancing “exploring new data” and “exploiting historical data.” Multi-armed bandits (MABs) have gained prominence in recent years for their ability to address this balance in uncertain environments while maintaining computational efficiency. This paper provides a comprehensive review of MAB-based recommendation methods structured around the key components of the MAB framework. We begin by analyzing how three classical MAB algorithms balance exploration and exploitation, framing the recommendation task as an MAB problem, and propose a classification method based on the core framework components for fine-grained algorithm analysis. We then examine existing methods that optimize four critical components: Agent, Action, Context, and Reward. In addition, we review nine commonly used datasets and six evaluation metrics, summarizing the Regret upper bounds and time complexity of state-of-the-art methods. To support empirical comparison, we reproduce and evaluate five representative algorithms on three popular public datasets. Finally, we identify key research challenges in MAB-based recommendations and outline promising directions for future work.</p>