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Worldwide carbon dioxide (CO2) emissions targets are unlikely to be met without large scale geological CO2 storage, with much of the storage capacity found in saline aquifers. The key aim of carbon sequestration is the long-term or permanent storage of CO2 within the sub-surface, minimising the potential for CO2 leakage back to the surface. When CO2 is injected into a saline aquifer, it rises until it reaches an impermeable horizon, known as a caprock, where it subsequently spreads out due to buoyancy forces. While the CO2 is spreading, the chance of encountering potential leakage pathways increases and the potential rates of trapping also increase. In this dissertation, I combine reduced-order fluid models and geophysical data to understand the controls on the rate of trapping and CO2 leakage in saline aquifers. Chapter 1 outlines the broader context of CO2 sequestration, both in terms of physical processes, observations, and policy implications. In Chapter 2, I investigate the rate at which CO2 dissolves when injected into heterogeneous saline aquifers. As CO2 dissolves into brine, the density of the brine is increased, thereby acting as a mechanism for the stable trapping of CO2. CO2 injected into heterogeneous geological formations results in preferential migration along high permeability pathways, thus increasing the CO2-water interfacial area and enhancing dissolution rates. I analyse the rate at which free-phase CO2 propagates in layered reservoirs and the quantity of CO2 dissolved, showing that for reservoirs with finely bedded strata, over 10% of the injected CO2 can dissolve in a year. In Chapter 3, I investigate the potential for fault zones, which are localised planes of brittle deformation, to act as leakage pathways which transect low permeability structural seals. I develop an analytical model to describe the dynamics of leakage through a fault zone cross-cutting multiple aquifers and seals. This is tested against a set of porous media tank experiments and applied to a naturally occurring CO2-charged aquifer system at Green River, Utah. In Chapters 4 and 5, I combine seismic observations of a carbon sequestration project with numerical modelling to investigate the extent to which reduced-order models can accurately predict CO2 movement in heterogeneous aquifers at the Otway CO2 sequestration project in Victoria, Australia. I analyse seismic measurements of the motion of CO2 in the stage 2C trial, in which 15,000 tonnes of CO2-rich gas was injected into a saline aquifer at 1.5 km depth. The geometry of the reservoir and extent and thickness of the CO2 current is extracted from a series of time-lapse seismic surveys. I solve a gravity current model which accounts for topographic gradients in the caprock and incorporates residual trapping of CO2 numerically to model the observed spreading. This vertically-integrated model is inverted to find bulk reservoir properties that best match the modelled and measured CO2 distributions. The sensitivity of the model to changes in bulk properties and topographic gradients is investigated. In the concluding Chapter 6, I review the use of reduced-order physical modelling in describing the movement, trapping and leakage behaviour of CO2 in geological porous media, with application to field scale CO2 sequestration projects.