Spacecraft trajectory optimization has always been a determining factor in successful space missions as it should be precise and efficient in automatically exploiting new opportunities present in the complex and dynamic environment. Traditional optimization algorithms cannot meet the increasing demand for fast computation, adaptation ability, or overcoming real-time constraints. A recently developed technique called reinforcement learning is quite promising in dealing with such issues by proposing innovative solutions for trajectory optimization. This paper surveys cutting-edge reinforcement learning solutions for optimizing spacecraft trajectory problems. Comprehensive and pragmatic analysis based on different aspects of currently available solutions, and concise reports are generated to get the latest update on this field, as well as provide reference on designing future-related solutions. The survey suggests that more efforts from the research field should be spent on reinforcement learning solutions especially when applied in the real mission scenario because there are still many challenges unattended by the community that were pointed out before being delivered at the end-user level.