The use of reinforcement learning (RL) for dynamic obstacle avoidance (DOA) algorithms and path planning (PP) has become increasingly popular in recent years. Despite the importance of RL in this growing technological era, few studies have systematically reviewed this research concept. Therefore, this study provides a comprehensive review of the literature on dynamic reinforcement learning-based path planning and obstacle avoidance. Furthermore, this research reviews publications from the last 5 years (2018–2022) to include 34 studies to evaluate the latest trends in autonomous mobile robot development with RL. In the end, this review shed light on dynamic obstacle avoidance in reinforcement learning. Likewise, the propagation model and performance evaluation metrics and approaches that have been employed in previous research were synthesized by this study. Ultimately, this article’s major objective is to aid scholars in their understanding of the present and future applications of deep reinforcement learning for dynamic obstacle avoidance.