The first comprehensive structural study of the Ni-U-O system is reported. Single crystals of alpha-NiUO4, beta-NiUO4, and NiU3O10 were synthesized, and their structures were refined-using synchrotron single-crystal X-ray diffraction data supported by X-ray absorption spectroscopic measurements. alpha-NiUO4 adopts an orthorhombic structure in space group Pbcn and is isostructural to CrUO4 containing corrugated two-dimensional (2D) layers of corner-sharing UO6 polyhedra and edge-sharing one-dimensional (1D) zigzag alpha-PbO2 rutile-like chains of NiO6 polyhedra in the [001] direction. beta-NiUO4 is isostructural to MgUO4 and has an orthorhombic structure in space group Ibmm, which contains alternating 1D chains of edge-sharing UO6 and NiO6 polyhedra in the [001] direction as in regular TiO2 rutile. NiU3O10 forms a triclinic structure in space group P (1) over bar and is isostructural with CuU3O10, where it forms a three-dimensional (3D) framework structure built through a mixture of UO6 and UO7 polyhedra in which the NiO6 polyhedra sit isolated within the framework. X-ray absorption near-edge structure (XANES) measurements, conducted using XANES mapping of single crystals, support the presence of hexavalent uranium in the three structures. The polymorphs of NiUO4 were found to only form under high-pressure and high-temperature conditions (>= 4 GPa and 700 degrees C). It is argued that this is a consequence of the relative size difference between the Ni2+ and U6+ cations, where the Ni2+ cation is effectively too small for the Ibmm structure and too large for the Pbcn structure to form under ambient pressure conditions. This does not appear to be an issue for NiU3O10, which forms under ambient pressure conditions, where NiO6 polyhedra sit isolated within the framework of 3D connected UO6/UO7 polyhedra. Synthesis conditions indicate that beta-NiUO4 is the preferred higher-pressure phase and that the transformation to this occurs irreversibly at a temperature between 950 and 1000 degrees C, when P = 4 GPa. The routes toward the synthesis of the oxides and the associated structural and spectroscopic results are described with respect to the structural chemistry of the Ni-U-O system, the larger AUO(4) family of oxides (A = divalent or trivalent cation), and also their relation to the rutile-related family of oxides.