Foundation models are driving a paradigm shift in robotic intelligence, moving beyond low-level action prediction to goal-directed orchestration of data collection, model training, task planning, and real-world execution. We characterize this emerging paradigm as an agentic robots, in which agents reason over human instructions, interact with robotic environments, rectify execution errors autonomously, and dynamically adjust operational strategies. Although this field develops fast, current studies are not well connected. Researchers have no consistent view of how to combine different agentic functions into a complete robot system. This paper provides a unified overview of existing research on agentic robots. We first trace the development from robot policies to agentic systems, covering vision-language-action models, world models, and world-action models. We then clarify the definition and scope of agentic robots and organize existing research into seventeen categories across four functional domains: Model, Data, Environment, and Harness. Across these domains, we examine how agents shape model learning and robot decisions, collect and curate robot data, construct worlds, tasks, and tests for learning and evaluation, and organize capabilities for robot use. Finally, we discuss open challenges and outline directions for future research. Looking forward, we hope this work contributes to a clearer understanding of agentic robots and supports new approaches to making them more capable, reliable, and adaptive.

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