Carbon capture and storage (CCS) involves the injection of CO2 into subsurface environments for long term storage. One example is the Sleipner field below the North sea in Norway, which has operated since 1996. However, a major challenge in accurately modelling the dynamics of CCS lies in the geological complexity of these subsurface environments, where real geological systems are far from the ideal homogeneous, isotropic porous media commonly assumed in simple mathematical models. This lecture addresses different approaches towards incorporating geospatial complexity into modelling CO2 flows, transport, and storage behaviour. The remainder of the lecture discusses the impact of thermal heat transfer and reaction fronts on injection front dynamics and ends with a brief note on the morphological evolution of viscous fingers.