Applications of ceria, CeO2 in catalysis and solid oxide fuel cells arise from the relative ease with which oxygen vacancies are formed, producing reactive sites or facilitating ionic diffusion. In this paper, we consider modelling oxygen vacancies in bulk ceria and on the low index surfaces, as well as oxygen vacancy migration in bulk. We apply density functional theory (DFT), corrected for on-site Coulomb interactions, DFT+U, since DFT is unable to describe correctly the electronic structure of defective ceria. We obtain a description of oxygen vacancies consistent with experiment, with localisation of charge on the Ce ions neighbouring the vacancy site. Confirming classical interatomic potential results, the oxygen vacancy formation energy in reduced on surfaces compared to bulk. An elastic band approach is applied to the study of vacancy migration in bulk ceria, yielding a diffusion path and energy barrier which are compared with previous studies.