Agentic artificial intelligence is transforming enterprise metadata management from rule-based automation to goal-directed systems capable of discovering, interpreting, connecting, and governing metadata across heterogeneous data estates. This review evaluates how autonomous agents can facilitate metadata discovery, sensitive-data classification, semantic enrichment, lineage reconstruction, enterprise catalog maintenance, and stewardship, while maintaining accountability to established data-governance frameworks. A structured integrative review of DOI-verified peer-reviewed literature connects three typically distinct research streams: enterprise metadata and data catalogs, knowledge graphs and provenance, and large-language-model-based autonomous agents. The synthesis indicates that the most effective near-term approach is policy-constrained orchestration, where specialized agents propose metadata changes, ground decisions in catalogs and knowledge graphs, preserve evidence, and escalate significant actions to stewards. DAMA-oriented management domains provide the operational model for ownership, quality, architecture, metadata, and governance, while Saudi Arabia's NDMO context elevates requirements for classification, traceability, control evidence, and institutional accountability. The review introduces an auditable agentic metadata architecture and an autonomy-assurance loop. It concludes that enterprise value relies on provenance-preserving execution, confidence-aware escalation, semantic interoperability, human override, measurable metadata quality, and governance controls that recognize agent actions as auditable events rather than invisible automation.