In the current proposal for the disposal of high-level radioactive waste in Sweden (the so-called KBS3 model), the nuclear waste will be stored in sealed copper canisters that are to be deposited in the bedrocks 500 meters underneath Forsmark. The copper canister will act as a corrosion barrier and is designed to prevent ground water from coming into contact with the nuclear waste for a time period of 100’000 years. In order to assist in the assessment of the copper material, we have conducted a variety of computational studies. These include the evaluation of copper corrosion under aqueous and oxygen-free conditions: a topic that has been intensely debated lately due to recent experimental results that seemingly contradicts the established thermodynamics of the copper-water system. To this end we have e.g. scrutinized the importance of including a sufficiently large water solvation shell in the computational model for the study of copper nanoparticle oxidation. We have also investigated the water structure and surface oxidation of copper as well as copper-oxide surfaces, in close collaboration with experimental groups. In the long perspective the most important corrosion mode for the nuclear waste disposal will, however, be sulfide-controlled corrosion. For this purpose we have analyzed the critical initial steps of the Cu2O sulphidation process, which are indicative of whether the ongoing corrosion will be homogenous (wanted) or local (unwanted). Our work in this field has also involved theoretical development, and in my talk I will include discussions on local reactivity tools for assessing adsorption and catalytic/corrosive active sites on particles and surfaces.