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, a central question is whether operational assurance develops commensurately with the authority granted to them. This survey examines that question through a structured, evidence-stratified review of agentic NetOps and AIOps, spanning directly evaluated LLM systems, operational mechanisms, transferred evidence, and normative guidance. 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 indicates 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 develop a workflow-level evaluation framework covering evidence quality, tool use, policy and invariant compliance, staged execution, recovery, calibration, cost, and human intervention, together with a threat model for prompt-borne attacks, compromised operational evidence, excessive agency, privilege boundaries, and auditability. The resulting view treats agentic NetOps and AIOps as constrained operational control, in which increasing autonomy requires correspondingly stronger evidence, independently enforced safeguards, and recovery mechanisms.

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