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The Gravity Recovery and Climate Experiment (GRACE) and its successor GRACE Follow-On (GRACE-FO) have revolutionized large-scale hydrological monitoring by providing monthly estimates of Terrestrial Water Storage Anomalies (TWSA) at near-global coverage. However, two fundamental constraints limit their operational utility: (i) temporal discontinuities arising from instrument gaps, orbital maneuvers, and the 11-month inter- mission hiatus (July 2017–May 2018); and (ii) the challenge of forecasting future storage states to support drought early warning and sustainable groundwater management. Both constraints are particularly acute in arid and semi-arid regions (ASARs), where the combination of high hydroclimatic variability, sparse in-situ monitoring networks, and critical groundwater dependence demands both continuous and predictive satellite gravimetry products. This paper presents a comprehensive review of peer-reviewed studies published between 2010 and 2026, synthesizing methods for GRACE gap-filling and TWSA/Groundwater Storage Anomaly (GWSA) forecasting, with a dedicated focus on ASAR applications and challenges. Gap-filling approaches are classified into three categories: statistical/empirical, data assimilation, and machine learning (ML). Forecasting methods span process-based, statistical, and deep- learning frameworks. The review reveals a strong trend toward hybrid physics-ML models for both tasks, driven by their ability to integrate physical constraints with the flexible, data-driven representation of complex hydroclimatic processes. Critical research gaps are identified, including the scarcity of ASAR-validated gap-filling benchmarks, the limited lead times achievable in deep learning forecasting applications, and the persistent challenge of isolating anthropogenic groundwater depletion from climatically driven TWSA variability. Future research directions emphasizing probabilistic forecasting, multi-source data fusion, and regionally tailored model calibration are proposed.