A rigorous study is presented of the physical processes related to X-Ray photoelectron spectroscopy, XPS, in the 4f level of U oxides, which, as well as being of physical interest in themselves, are representative of XPS in heavy metal oxides. In particular, we present compelling evidence for a new view of the screening of core-holes that extends prior understandings. Our analysis of the screening focuses on the covalent mixing of high lying U and O orbitals as opposed to the, more common, use of orbitals that are nominally pure U or pure O. It is shown that this covalent mixing is quite different for the initial and final, core-hole, configurations and that this difference is directly related to the XPS satellite intensity. Furthermore, we show that the high-lying U d orbitals as well as the U(5f) orbital may both contribute to the core-hole screening, in contrast with previous work that has only considered screening through the U(5f) shell. The role of modifying the U-O interaction by changing the U-O distance has been investigated and an unexpected correlation between U-O distance and XPS satellite intensity has been discovered. The role of flourite and octahedral crystal structures for U(IV) oxides has been examined and relationships established between XPS features and the covalent interactions in the different structures. The physical views of XPS satellites as arising from shake processes or as arising from ligand to metal charge transfers are contrasted; our analysis provides strong support that shake processes give a more fundamental physical understanding than charge transfer. Our theoretical studies are based on rigorous, strictly ab initio determinations of the electronic structure of embedded cluster models of U oxides with formal U(VI) and U(IV) oxidation states. Our results provide a foundation that makes it possible to establish quantitative relationships between features of the XPS spectra and materials properties.