The electronic structure of cerium oxide is investigated here using a combination of ab initio one-electron theory and elements from many-body physics, with emphasis on the nature of the 4f electron shell of cerium ions. We propose to use the hybridization function as a convenient measure for the degree of localization of the 4f shell of this material, and observe that changing the oxidation state is related to distinct changes in the hybridization between the 4f shell and ligand states. The theory reveals that CeO2 has essentially itinerant 4f states, and that in the least oxidized form of ceria, Ce2O3, the 4f states are almost (but not fully) localized. This conclusion is supported by additional calculations based on a combination of density functional theory and dynamical mean field theory. Most importantly, our model points to the fact that diffusion of oxygen vacancies in cerium oxide may be seen as polaron hopping, involving a correlated 4f electron cloud, which is located primarily on Ce ions of several atomic shells surrounding the vacancy.