In recent years, Unmanned Aerial Vehicles (UAVs) have attracted a lot of attention due to their flexibility and high mobility. Nowadays, UAVs have been widely used in various fields, such as military fields and social fields. However, due to the increasingly complex environments faced by UAVs and the rising demands on UAV systems, traditional UAV control methods are no longer able to achieve efficient control of UAVs under multi-constraint situations. Reinforcement Learning (RL), as an emerging robot control technology, is well suited to the needs of UAV systems in terms of its ability to interact with and learn from the environment. Therefore RL-based UAV systems are gradually becoming a new trend in research. Nonetheless, as a new research field, it faces many challenges, such as high dimensional spaces and dynamic environments. It is necessary to provide a comprehensive overview and analysis of existing specific RL methods applied to UAV systems, and to understand the challenges as well as possible solutions for RL-based UAV systems. In this paper, we first provide a comprehensive overview and summary of the application of RL in different UAV application scenarios based on the classification of RL methods. After that, we systematically analyze the challenges and solutions faced by RL applied to UAV systems given the existing relevant literature. Finally, we discuss the potential research directions for RL-based UAV systems.