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It has been demonstrated in previous experimental and computational work that doping CeO2 with transition metals is an effective way of tuning its properties. However, each previous study on CeO2 doping has been limited to a single or a few dopants. In this paper, we systematically study the formation energies, structural stability and electronic properties of CeO2 doped with the entire range of the ten 3d transition metals using density functional theory (DFT) calculations at the hybrid level. The formation energies of oxygen vacancies, and their effects on electronic properties, were also considered. It is found that most of the 3d transition metal dopants can lower the band gap of CeO2, with V and Co doping significantly reducing the band gap to less than 2.0 eV. Furthermore, all of the dopants can lower the formation energy of oxygen vacancies, and those with higher atomic numbers, particularly Cu and Zn, are most effective for this purpose. The electronic structures of doped CeO2 compensated by oxygen vacancies show that the presence of oxygen vacancies can further lower the band gap for most of the dopants, with V-, Cr-, Fe-, Co-, Ni-, and Cu-doped CeO2 all having band gaps of less than 2.0 eV. These results suggest that doping CeO2 with 3d transition metals could enhance the photocatalytic performance under visible light and increase the oxygen vacancy concentration, and they could provide a meaningful guide for the design of CeO2-based materials with improved photocatalytic and catalytic performance as well as enhanced ionic conductivity.