High-precision, long-endurance navigation remains a central bottleneck for autonomous underwater vehicles (AUVs) operating in GNSS-denied, acoustically constrained, and dynamically disturbed marine environments. This manuscript examines the complete sensing-mapping-estimation chain for underwater geomagnetic navigation. It distinguishes scalar and vector measurements; compares shipborne, towed, and AUV-mounted survey configurations, calibration requirements, platform-interference mitigation, and uncertainty sources; reviews global, regional, and local magnetic models; and evaluates nonlinear map-aided positioning. Existing approaches are organized into map-based matching, filter-aided navigation, geomagnetic simultaneous localization and mapping (SLAM), and matching-area adaptability assessment. Their assumptions, data requirements, uncertainty treatment, accuracy evidence, and computational burden are critically compared. Persistent gaps include magnetic cleanliness, three-dimensional mapping, weak-feature-area observability, benchmark datasets, uncertainty quantification, and reproducible long-duration sea trials.