The escalating complexity of modern network infrastructures, characterized by the convergence of multi-cloud environments, microservices, and massive IoT deployments, has pushed traditional network monitoring beyond its structural limits. Traditional monitoring, which relies on static thresholds and reactive alerting, fails to provide the deep \"internal state\" visibility required for modern digital resilience. This review examines the paradigm shift toward AI-powered network observability systems. Unlike traditional monitoring, observability leverages high-cardinality telemetry data—including logs, metrics, and traces—to enable the \"Unknown-Unknown\" discovery of system behaviors. By integrating Artificial Intelligence (AI) and Machine Learning (ML), these systems transition from simple data aggregation to \"Cognitive Insight\" engines. We categorize the core methodologies of AI-driven observability, including the use of unsupervised learning for real-time anomaly detection, Graph Neural Networks (GNNs) for mapping relational topologies, and Natural Language Processing (NLP) for parsing unstructured log telemetry. This article explores how these systems automate Root Cause Analysis (RCA) and enable \"Self-Healing\" network architectures. Furthermore, the review addresses critical challenges, such as the \"Data Silo\" problem, the computational overhead of real-time inference at the network edge, and the necessity for Explainable AI (XAI) to foster operator trust. By synthesizing recent breakthroughs in Deep Learning and AIOps, this paper provides a strategic roadmap for building \"Autonomous Observability\" frameworks. The findings suggest that AI-powered observability is the foundational technology required to manage the invisible complexity of the 6G and hyper-connected era, ensuring that network operations move from reactive troubleshooting to proactive, foresight-driven optimization.