Open RAN (O-RAN) exposes rich control and telemetry interfaces across the Non-RT RIC, Near-RT RIC, and distributed units, but also makes it harder to operate multi-tenant, multi-objective RANs in a safe and auditable manner. In parallel, agentic AI systems with explicit planning, tool use, memory, and self-management offer a natural way to structure long-lived control loops. This article surveys how such agentic controllers can be brought into O-RAN: we review the O-RAN architecture, contrast agentic controllers with conventional ML/RL xApps, and organise the task landscape around three clusters: network slice life-cycle, radio resource management (RRM) closed loops, and cross-cutting security, privacy, and compliance. We then introduce a small set of agentic primitives (Plan-Act-Observe-Reflect, skills as tool use, memory and evidence, and self-management gates) and show, in a multi-cell O-RAN simulation, how they improve slice life-cycle and RRM performance compared to conventional baselines and ablations that remove individual primitives. Security, privacy, and compliance are discussed as architectural constraints and open challenges for standards-aligned deployments. This framework achieves an average 8.83\% reduction in resource usage across three classic network slices.

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