Abstract: Carbon dioxide capture, utilization, and storage is now widely acknowledged as one of the most effective strategies to reduce atmospheric carbon emissions, as well as the key to advancing China's 2060 carbon neutrality target. The numerical simulation of the underlying T-H-M-C multi-field coupled risk analysis in reservoir-caprock systems is a critical technology for understanding the long-term process and demonstrating storage security during CO₂ geological storage. In the present study, we present a comprehensive review on the current research progress of numerical simulation on risk analysis under multi-field coupling during CO₂ geological storage. Firstly, we briefly review the research progress in the governing equations, in terms of stress equilibrium equation, mass conservation equation, energy conservation equation, chemical reaction equation, and constitutive equation. Meanwhile, we summarize various numerical coupling solutions, including full coupling, iterative coupling, loose coupling, explicit coupling, and pseudo coupling. Furthermore, we introduce the analysis methods of CO₂ leakage, ground deformation, fault activation, and fracture development. Finally, we provide insights into future research directions on the technical challenges which are addressed in the numerical modeling of CO₂ geological storage. Our research can provide a valuable reference for the study of CO₂ geological storage at site scale.