Carbon capture and storage (CCS) in deep geological formations is one possible option to mitigate the greenhouse gas effect by reducing CO2 emissions into the atmosphere. The assessment of the risks related to CO2 storage is an important task. Events such as CO2 leakage and brine displacement could result in hazards for human health and the environment. In this thesis, a systematic and comprehensive risk assessment concept is presented to investigate various levels of uncertainties and to assess risks using numerical simulations. Depending on the risk and the processes, which should be assessed, very complex models, large model domains, large time scales, and many simulations runs for estimating probabilities are required. To reduce the resulting high computational costs, a model reduction technique (the arbitrary polynomial chaos expansion) and a method for model coupling in space are applied. The different levels of uncertainties are: statistical uncertainty in parameter distributions, scenario uncertainty, e.g. different geological features, and recognized ignorance due to assumptions in the conceptual model set-up. Recognized ignorance and scenario uncertainty are investigated by simulating well defined model set-ups and scenarios. According to damage values, which are defined as a model output, the set-ups and scenarios can be compared and ranked. For statistical uncertainty probabilities can be determined by running Monte Carlo simulations with the reduced model. The results are presented in various ways: e.g., mean damage, probability density function, cumulative distribution function, or an overall risk value by multiplying the damage with the probability. If the model output (damage) cannot be compared to provided criteria (e.g. water quality criteria), analytical approximations are presented to translate the damage into comparable values. The overall concept is applied for the risks related to brine displacement and infiltration into drinking water aquifers. The uncertainties on all three levels are investigated in three approaches with different focus. The concept can also be applied to CO2 leakage or hazards related to other technologies in the subsurface such as methane storage or atomic waste disposal. In the second part of this thesis, uncertainty studies for two realistic storage formations (the pilot site Ketzin (Germany) and a realistic storage formation in the North German Basin) are performed to investigate the related uncertainties and to reduce them as much as possible. For the Ketzin site, history matching of the measurement data, is an important task for dynamic modeling and essential for future risk assessment. A systematic approach to fit the data set using inverse modeling is presented in this work. For future risk assessment for realistic sites, e.g. for the Ketzin site, the uncertainty studies and the history matching approach provide important information. Finally, CCS is discussed in the context of risk perception and the possible input of the risk assessment concept presented in this work is discussed. This work is a first attempt to connect the technical risk assessment for CO2 storage to the social science approach for risk assessment. It is bridging the gap between engineering and social sciences by integrating the technical quantification of risk into the wider context of a comprehensive risk governance model.