This work presents model development and model analyses of CO2 storage in deep saline aquifers. The goal has been two-fold, firstly to develop models and address the system behaviour under geological heterogeneity, second to tackle the issues related to problem scale as modelling of the CO2 storage systems can become prohibitively complex when large systems are considered. The work starts from a Monte Carlo analysis of heterogeneous 2D domains with a focus on the sensitivity of two CO2  storage performance measurements, namely, the injectivity index (Iinj) and storage efficiency coefficient (E), on parameters characterizing heterogeneity. It is found that E and Iinj are determined by two different parameter groups which both include correlation length (λ) and standard deviation (σ) of the permeability. Next, the issue of upscaling is addressed by modelling a heterogeneous system with multi-modal heterogeneity and an upscaling scheme of the constitutive relationships is proposed to enable the numerical simulation to be done using a coarser geological mesh built for a larger domain. Finally, in order to better address stochastically heterogeneous systems, a new method for model simulations and uncertainty analysis based on a Gaussian processes emulator is introduced. Instead of conventional point estimates this Bayesian approach can efficiently approximate cumulative distribution functions for the selected outputs which are CO2 breakthrough time and its total mass. After focusing on reservoir behaviour in small domains and modelling the heterogeneity effects in them, the work moves to predictive modelling of large scale CO2  storage systems. To maximize the confidence in the model predictions, a set of different modelling approaches of varying complexity is employed, including a semi-analytical model, a sharp-interface vertical equilibrium (VE) model and a TOUGH2MP / ECO2N model. Based on this approach, the CO2 storage potential of two large scale sites is modelled, namely the South Scania site, Sweden and the Dalders Monocline in the Baltic Sea basin. The methodologies developed and demonstrated in this work enable improved analyses of CO2 geological storage at both small and large scales, including better approaches to address medium heterogeneity. Finally, recommendations for future work are also discussed.