In this talk we discuss two topics. The first one is oxidation of UO2 and the second one is diffusion of fission gases in UO2±x and its implications for fission gas release models. Formation of hyperstoichiometric uranium dioxide compounds, UO2+x, derived from the fluorite structure was investigated by density functional theory (DFT) calculations. Oxidation was modeled by adding oxygen atoms to UO2 fluorite supercells. A similar approach was applied for studying reduction of U3O8. In agreement with the experimental phase diagram we identify stable line compounds at the U4O9-y and U3O7 stoichiometries. Additionally, we also found a new compound of the U3O7.3333 stoichiometry to be stable between U3O7 and U3O8. The calculated low-temperature phase diagram indicates that the fluorite-derived compounds are favored up to the UO2.5, i.e. as long as the charge-compensation for adding oxygen atoms occurs via formation of U5+ ions. Once U6+ ions are required to achieve overall charge neutrality, the U3O8-y phase becomes more stable. According to our calculations the most stable fluorite UO2+x phases at low temperature (0 K) are based on split quad-interstitial oxygen clusters. This cluster contains four excess and two displaced regular fluorite oxygen ions. It shares some features with the cuboctahedral cluster that is used in existing crystallographic models of U4O9 and U3O7, but the details are different. In order to better understand these discrepancies, the new structure models obtained from our simulations are analyzed in terms of existing neutron diffraction data. Finally, we discuss the importance of cluster formation for oxygen diffusion in UO2+x. In order to better understand bulk fission gas behavior in UO2±x we calculate the relevant activation energies using DFT techniques. Here we focus on Xe, since it is the most important fission gas in UO2 nuclear fuels. By analyzing a combination of Xe solution thermodynamics, migration barriers and the interaction of dissolved Xe atoms with U vacancies, we demonstrate that Xe diffusion predominantly occurs via a vacancy-mediated mechanism. Next we investigate Xe transport on the (111) UO2 surface, which is motivated by the formation of small voids partially filled with fission gas atoms (bubbles) in UO2 under irradiation. Surface diffusion could be the rate-limiting step for diffusion of such bubbles, which is an alternative mechanism for mass transport in these materials. As expected, the activation energy for surface diffusion is significantly lower than for bulk transport. These results are further discussed in terms of engineering-scale fission gas release models.