The research for radiation-resistant compounds with fluorite related structure is a challenging area of research for developing reliable nuclear energy systems. Those systems, and advanced fuels in particular, require a sound understanding based on reliable experiments and numerical modelling in order to ensure their safe behaviour throughout the fuel life cycle, from fabrication to end of life storage. The problem of understanding and developing a predictive capability for the evolution of fuels is a challenging one, even for features apparently simple as oxidation. Uranium oxides have deceptively simple approximate chemical formulas that actually betray their extremely complex structural features and their propensity to form nonstoichiometric phases of composition UO2+x: in these phases U atoms exhibit multiple charge states and configurations. We would try to summarize a multidisciplinary effort to characterize the structural features of laboratory prepared UO2+x systems (0