Abstract: To address the problems of distinct engineering scenarios, unclear physical implications of monitoring data, and insufficient connection between prediction models and stability identification targets during the operation of underground energy storage spaces, the monitoring data characteristics, applicable conditions of prediction methods, and physics–data fusion approaches for surrounding rock stability are analyzed based on the relationship of “monitoring response–physical constraint–stability state”. Salt cavern energy storage spaces and hard rock underground caverns are taken as the main objects, and abandoned mines and goafs are used as supplementary scenarios under complex disturbance conditions. Based on differences in cavern-forming method, surrounding rock medium, operating pressure regime, and support structure, the engineering implications of monitoring information, including displacement, strain, pressure, temperature, seepage, microseismicity, acoustic emission, sonar cavity measurement, and geophysical detection, are analyzed, and the roles of continuous time-series data, event-based data, and spatial imaging data in stability identification are clarified. The analysis shows that the stability of salt cavern energy storage spaces is mainly controlled by salt rock creep, cavity convergence, interlayer seepage, pressure cycling during injection and withdrawal, and sealing evolution. Their monitoring data usually show long-period, strongly trending, and slowly varying responses, so prediction should focus on deformation rate, cavity shape variation, and pressure operation boundaries. Hard rock underground caverns are affected by high internal pressure cycling, temperature–pressure coupling, local damage propagation, and interaction between surrounding rock and support structures. Their monitoring data are more likely to show staged fluctuations, multi-parameter coupling, and sudden anomalies, so stability identification should focus on damage activity concentration, support stress variation, and abnormal response recognition. Abandoned mines and goafs are affected by historical mining disturbance and spatial structural heterogeneity, and their monitoring data are often accompanied by missing measuring points, superposed noise, and abrupt responses; therefore, prediction logic for salt caverns or hard rock caverns should not be directly applied. The key to stability prediction of underground energy storage surrounding rock is not simply comparing algorithm accuracy, but whether the prediction results can reflect surrounding rock mechanical response laws and satisfy operating boundary constraints. Monitoring data processing should shift from general denoising, standardization, and fitting optimization to feature construction oriented to stability state identification. Prediction models should incorporate constitutive relationships of surrounding rock media, operating pressure and temperature boundaries, seepage conditions, and stability criteria to constrain the evolution trend and reasonable range of prediction results. Model evaluation should consider prediction accuracy, physical consistency, anomaly identification capability, and warning interpretability, thereby improving the engineering applicability of dynamic stability assessment and risk warning during operation.