Connected and automated vehicles (CAVs) require multiple tasks in their seamless maneuverings. Some essential tasks that require simultaneous management and actions are motion planning, traffic prediction, traffic intersection management, etc. A few of them are complex in nature. Multi-agent reinforcement learning (MARL) can solve complex problems involving simultaneous controls. Recently, many researchers applied MARL in such applications. However, there is a lack of extensive surveys on the ongoing research to identify the current problems, proposed methods, and future research directions in MARL for CAVs. This paper provides a comprehensive survey on MARL for CAVs. A classification-based paper analysis is performed to identify the current developments and highlight the various existing research directions. Finally, the challenges in current works are discussed, and some potential areas are given for exploration to overcome those challenges. Future readers will benefit from this survey and can apply the ideas and findings in their research to solve complex problems.