Assessing the long-term safety of geological CO₂ storage remains a critical technical challenge. CO₂ migration in porous media is governed by the coupling of multiphase flow, capillary trapping, dissolution, geochemical reactions, and geomechanical effects. In addition to geophysical monitoring methods, experimental and mathematical models can estimate CO₂ leakage volumes and associated risks by simulating fluid transportation processes. This perspective offers a comprehensive comparison of the recent experimental studies, physics-based models, and data-driven approaches for evaluating CO₂ storage safety. Laboratory investigations provide fundamental insights into plume evolution and trapping mechanisms. Analytical and semi-analytical models generate rapid storage capability screening. Numerical simulators serve as essential tools for evaluating long-term storage performance. Data-driven methods can accelerate computational-demanding numerical workflows and support uncertainty quantification. Based on the strengths and limitations of the physics-based and data-driven approaches, this paper further identifies future research directions in experimental design and mathematical modeling for CO₂ storage safety assessment.