Geological Carbon Storage (GCS) is considered as one of the key techniques to reduce the rate of atmospheric emissions of CO2 and thereby to contribute to controlling the global warming. A successful application of a GCS project requires the capability of the formation to trap CO2 for a long term. In this context, processes related to CO2 trapping and also possible leakage of CO2 to the near surface environment need to be understood. The overall aim of this thesis is to understand the flow and transport of CO2 through porous media in the context of geological storage of CO2. The entire range of scales, including the pore scale, the laboratory scale, the field experiment scale and the industrial scale of CO2 injection operation are addressed, and some of the key processes investigated by means of experiments and modeling.  First, a numerical model and laboratory experimental setup were developed to investigate the CO2 gas flow, mimicking the system in the near-surface conditions in case a leak from the storage formation should occur. The system specifically addressed the coupled flow and mass transport of gaseous CO2 both in the porous domain as well as the free flow domain above it. The comparison of experiments and modelling results showed a very good agreement indicating that the model developed can be applied to evaluate monitoring and surface detection of potential CO2 leakage. Second, the field scale CO2 injection test carried out in a shallow aquifer in Maguelone, France was analyzed and modeled. The results showed that Monte Carlo simulations accounting for the heterogeneity effects of the permeability field did capture the key observations of the monitoring data, while a homogeneous model could not represent them. Third, a numerical model based on phase-field method was developed and model simulations carried out addressing the effect of wettability on CO2-brine displacement at the pore-scale. The results show that strongly water-wet reservoirs provide a better potential for the dissolution trapping, due to the increase of interface between CO2 and brine with very low contact angles. The results further showed that strong water-wet conditions also imply a strong capillary effect, which is important for residual trapping of CO2. Finally, numerical model development and model simulations were carried out to address the large scale geological storage of CO2 in the presence of impurity gases in the CO2 rich phase. The results showed that impurity gases N2 and CH4 affected the spatial distribution of the gas (the supercritical CO2 rich phase), and a larger volume of reservoir is needed in comparison to the pure CO2 injection scenario. In addition, the solubility trapping significantly increased in the presence of N2 and CH4.