At room temperature UO2 assumes the fluorite structure with both uranium and oxygen atoms vibrating isotropically about their equilibrium positions. At higher temperatures (> 400 K) this model must be modified to account for the anharmonic, anisotropic contribution of the oxygen atoms to the Bragg intensities. Up to 1300 K the uranium atoms continue to vibrate isotropically. On oxidation of UO2 to UO2+x, defect clusters are formed in the oxygen sublattice. At x= 0.12 diffraction studies indicate that the configuration of the cluster is 2 : 2 : 2, i.e. consisting of two vacant oxygen sites, two interstitial oxygens displaced away from the cubic-coordinated interstitial sites along 〈110〉 and two oxygens displaced along 〈111〉. The uranium sublattice is not disturbed by the rearrangement of atoms in the oxygen sublattice. At the limiting composition of UO2.25, or U4O9, the oxygen clusters link together into an ordered superlattice structure. Many attempts have been made (using X.r.d., n.d., e.d. and X.p.s.) to solve this structure, and several incorrect solutions have been published. There are three closely related phases of U4O9, α, β and γ, and of these the crystal structure of the beta phase only is known, which was determined from neutron-diffraction data. The clusters in β-U4O9 are not like those in UO2.12. Each cluster consists of an octahedral arrangement of six UO8 square antiprisms, which share corners to enclose a cubo-octahedron of anions. The composition of such a cluster with an oxygen at the centre is U6O37, and the overall composition is U4O9–y where y= 0.0625. Further progress in understanding the nature of the defect clusters in UO2+x and U4O9 requires a combined attack with the methods of neutron scattering and of computer simulation.