Large language models (LLMs) are increasingly being used in network operations (NetOps) and artificial intelligence for IT operations (AIOps) for tasks ranging from telemetry retrieval and incident diagnosis to configuration planning and bounded remediation. As these systems acquire greater access to operational tools, the central question is no longer only what an LLM can do, but whether operational assurance increases commensurately with the authority granted to it. This survey examines that question through a structured, evidence-stratified review of agentic NetOps and AIOps. We organise the field around autonomy, tool scope, evidence traces, assurance controls, evaluation, security, and governance, and introduce an operational assurance contract that links each autonomy level to permitted tools, required evidence, independent gates, execution budgets, rollout and rollback duties, and audit requirements. The synthesis reveals a capability--assurance gap: evidence is comparatively strong for read-oriented assistance and tool-grounded diagnosis, but becomes substantially less complete as systems approach configuration change, bounded execution, and closed-loop operation. We therefore argue that evaluation should move beyond static question answering and model accuracy towards workflow-level assessment of evidence quality, tool use, policy and invariant compliance, staged execution, recovery, calibration, cost, and human intervention. We also examine prompt-borne attacks, poisoned or stale operational evidence, excessive agency, privilege boundaries, and weak auditability. Taken together, the survey frames agentic NetOps and AIOps as constrained operational control, in which useful autonomy depends on independently enforced assurance rather than model capability alone.

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