Due to the continuing consumption of fossil fuels, a large amount of CO_2 is emitted into the atmosphere, leading to global warming, sea level rising and other global climate problems. CO_2 geological storage is one of the most promising techniques for reducing CO_2 emission. However, this approach may induce a series of geomechanical issues, such as ground surface deformation, damage of the cap-rock integrity and existing fault activation. In order to reduce the safety risk from the CO_2 geological storage, theoretical analysis, numerical simulation and response surface method are all applied to solve these geomechanical issues. At present, numerical simulation is the most widely used option on account of its exceptional performances in solving multi-field coupling problems associated with large-scale and complex geometry model. The aim of this paper is to provide a comprehensive review of numerical analysis approaches for analyzing the geomechanical issues induced by CO_2 geological storage. First, a brief introduction is given about the thermo-hydro-mechano-chemical (THMC) coupling theory of porous media, and the classifications of the numerical simulation methods for settling the multi-field coupling problems are discussed; then, a review of research status about settling geomechanical issues based on numerical modeling is presented in detail; finally, the difficulties of the numerical simulation in solving these geomechanical issues are discussed, from which several suggestions for improvement are offered.