Agentic chip design combines large language models with electronic design automation (EDA) tools to plan, execute, and revise design operations. Its effectiveness depends on how an agent translates requirements into executable tasks, interprets diagnostic information, and coordinates changes across design stages. This survey examines these relationships across digital design, agent architectures, EDA algorithm and tool development, and evaluation, with additional coverage of analog, mixed-signal, and radio-frequency applications. We compare agentic chip-design methods through the design representations they modify, the feedback used to select revisions, and the procedures used to check correctness and implementation quality. The analysis shows that broader agent control over designs and EDA software expands optimization opportunities while increasing the need to manage dependencies and verify changes across the design flow. We also compare benchmarks and evaluation methods, focusing on functional correctness, implementation quality, and computational cost. These comparisons identify research directions in specification interpretation, failure diagnosis, repository-level integration, cross-stage optimization, and efficient tool use. By synthesizing these findings, this survey aims to guide the research community in developing and evaluating more reliable and efficient chip-design agents.