Research on mixed oxide compounds of Uranium with fluorite-related structure is important for developing reliable and safe nuclear energy systems. These compounds can be source of controversy (e.g. MOX), though burning hazardous elements is a sensible way to dispose of them. Blending U and aliovalent atoms in the oxide fuel also occurs for controlling excess reactivity with burnable poisons, or for reducing fission gas release by controlling the microstructure. Fuels containing significant amounts of aliovalent elements require a sound understanding of their long range and local structures throughout the fuel life cycle (fabrication, operation, and end-of-life storage). Predicting these evolutions is challenging, even for changes occurring at moderate temperatures because they involve both O migration and cation reorganization. Uranium oxides have deceptively simple approximate chemical formulas betraying their complex structural features. To illustrate these problems we discuss selected systems, emphasizing the need to foster further experimental and theoretical work.