The electronic structure of neutral and charged O and Mg vacancies at the surface of MgO (F, F+, F2+, V, V-, and V2- centers) has been investigated by means of cluster models and ab initio wave functions. For each center we have determined the formation energy and the local geometrical relaxation. The distribution of the electrons in the vacancy has been analyzed through the calculation of charge density plots and, for paramagnetic centers, isotropic hyperfine coupling constants. The latter are in good agreement with the EPR data. On F+ surface centers the unpaired electron is largely localized in the vacancy; the corresponding eigenstate is in the band gap. On V- centers, on the contrary, the unpaired electron is delocalized over the surface O neighbors and the eigenstate is in the valence band. For the first time we have considered also O vacancies at edge sites. The energetics of the formation of these sites and their electronic structure is not too different from that of the corresponding centers on the terraces of MEG, thus reinforcing the hypothesis that edge F centers can exist on the surface of thermally activated MgO.