The two-sided matching market problem has attracted extensive research in both computer science and economics due to its wide-ranging applications in multiple fields. In various online matching platforms, market participants often have unclear preferences. As a result, a growing area of research focuses on the online scenario. Here, one-side participants (players) gradually figure out their unknown preferences through multiple rounds of interactions with the other-side participants (arms). This survey comprehensively reviews and systematically organizes the abundant literature on bandit learning in matching markets. It covers not only existing theoretical achievements but also various other related aspects. Based on the current research, several distinct directions for future study have emerged. We are convinced that delving deeper into these directions could potentially yield theoretical algorithms that are more suitable for real-world situations.