Geological storage of carbon dioxide (CO2) in deep saline aquifers forms an integral part of many CO2 mitigation strategies. At depth CO2 is buoyant and therefore may leak into surface waters or the atmosphere. This talk will explore the rich multiphase fluid dynamics of CO2 propagation, providing constraints on the rate at which CO2 may leak from a storage site, and the dynamics of convective dissolution and capillary trapping, two leading processes by which CO2 may be stably trapped and stored within the subsurface.