Electronic design automation (EDA) is multi-stage and handoff-heavy, relying on transfers among humans, design artifacts, and multiple tools. LLM-based agents now participate in these transfers, yet the resulting research landscape is highly fragmented and lacks a unified perspective. This survey adopts the primary input--output pair as its organizing lens: for each agent system, we analyze its primary, supporting, and intermediate handoff objects and classify it according to the provenance of its primary input and the consumer boundary of its primary output. Intra-stage systems operate on objects within a single EDA stage, inter-stage systems transform EDA-native artifacts into forms usable by downstream stages, and extra-stage systems translate human intent into EDA artifacts. Based on this taxonomy, we survey 115 representative systems and examine them along multiple dimensions, including research trends, benchmarks, and model mechanisms. Finally, we outline an agentic EDA protocol roadmap and discuss open problems for future research.

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