Geological CO2 storage(GCS) is a technology for carbon emission-cut, by injecting anthropogenic CO2 for long-term storage into underground aquifers or depleted hydrocarbon reservoirs. Because of the uncertainties induced by geological site condition and human activities, injecting CO2 into the reservoir may lead to leakage through abandoned wells, faults, fractures, and the "weak zones" in the caprock. A comprehensive review on GCS-associated leakage and safety issues was made, based on an extensive investigation of both domestic and international literature. Leakage from a wellbore may occur through the annulus cement, well plugs or the fracture zone of the contact rocks, due to chemical corrosion and/or mechanical failure. Injecting massive amount of CO2 into reservoirs may induce fractures in the seal, activation of potential faults and their slip. Leakage of CO2 along faults/fractures is mainly affected by factors such as the effective permeability and fracture aperture. Leakage through the caprock can be seepage, diffusive or one that occurs through fissures. The diffusive leakage through the caprock should not be neglected when assessing leakage for large-scale GCS projects. Leakage of CO2/brine into the overlying aquifer causes its variation in geochemistry such as a lower pH, higher salinity, more ions, or even the presence of free CO2. Monitoring of pressure and sampling in the overlying aquifer can be effective to identify CO2 leakage from the underlying reservoir. Research on GCS-associated leakage is very limited, with a particular lack of quantitative studies in China.