Carbon capture and storage (CCS) is the only viable technology to mitigate carbon emissions while allowing continued large-scale use of fossil fuels. The storage part of CCS involves injection of carbon dioxide, captured from large stationary sources, into deep geological formations. Deep saline aquifers have the largest identified storage potential, with estimated storage capacity sufficient to store emissions from large stationary sources for at least a century. This makes CCS a potentially important bridging technology in the transition to carbon-free energy sources. Injection of CO 2 into deep saline aquifers leads to a multicomponent, multiphase flow system, in which geomechanics, geochemistry, and nonisothermal effects may be important. While the general system can be highly complex and involve many coupled, nonlinear partial differential equations, the underlying physics can sometimes lead to important simplifications. For example, the large density difference between injected CO 2 and brine may lead to relatively fast buoyant segregation, making an assumption of vertical equilibrium reasonable. Such simplifying assumptions lead to a range of simplified governing equations whose solutions have provided significant practical insights into system behavior, including improved estimates of storage capacity, easy-to-compute estimates of CO 2 spatial migration and pressure response, and quantitative estimates of leakage risk. When these modeling studies are coupled with observations from well-characterized injection operations, understanding of the overall system behavior is enhanced significantly. This improved understanding shows that, while economic and policy challenges remain, CO 2 storage in deep saline aquifers appears to be a viable technology and can contribute substantially to climate change solutions.