Abstract
Recent years have witnessed a rapid proliferation of learning, control, and planning algorithms for embodied AI. However, grouping methods by model family or learning paradigm often separates approaches serving the same behavioral function, hindering comparison. To address this gap, this survey classifies robotic manipulation research into three functional levels: sensorimotor behavior, reusable units, and task organization. This functional perspective brings together reinforcement learning approaches, vision-language-action models, world models, and code-as-policy methods. The taxonomy supports comparison within functional categories and the transfer of ideas across approaches, offering insights for future algorithm development toward more adaptable embodied systems.