Motion planning in dynamic environments is a fundamental problem in robotics, aiming to generate safe and efficient paths, trajectories, or control actions in the presence of moving obstacles, uncertain predictions, and multi-agent interactions. It has broad applications in autonomous driving, service robotics, warehouse logistics, human-robot collaboration, crowd navigation, and multi-robot systems. This survey reviews representative works published primarily between 2015 and 2025, with a particular focus on how recent learning-based advances extend, complement, or interact with classical planning foundations. We first revisit classical planning methods as algorithmic foundations and reference frameworks for learning-based extensions. We then propose a role-of-learning taxonomy that categorizes existing methods according to how learning participates in the planning pipeline, including direct policy learning, learning-augmented classical planning, hybrid planning, and training enhancement methods. For each category, we summarize the main problem settings, representative algorithms, key ideas, integration mechanisms, strengths, and limitations. We further analyze how observation representations, prediction uncertainty, interaction modeling, planner integration, safety constraints, and training strategies shape learning-based motion planning in dynamic environments. Finally, we discuss open challenges and future directions, including sim-to-real gap, safe and certifiable planning, dense crowd navigation, perception-planning coupling, and embodied AI.

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