Numerical simulations are essential to the understanding of the long-term geological storage of CO2. Physical modelling of geological storage of CO2 has been based on Darcy's law, together with the equations of conservation of mass and energy. Modelling and simulations can be used to predict where CO2 is likely to flow, to interpret the volume and spatial distribution of CO2 under storage conditions, and to optimise injection operations. The state of the art of physical modelling and numerical simulation of CO2 dispersion is briefly reviewed in this paper, which calls for more accurate and more efficient modelling approaches. A systematic evaluation of the numerical methods used and a comparison between the streamline based methods and the grid based methods would be valuable. Multi-scale modelling may prove to be of great value in predicting the long-term geological storage of CO2, while highly accurate numerical methods such as high-order schemes may be employed in numerical simulations of CO2 dispersion for local transport calculations. (C) 2011 Elsevier Ltd. All rights reserved.