We report the atomic and electronic structure of bulk BeO and the nonpolar BeO(10 1̄ 0) surface as resulting from density functional theory (DFT). Employing norm-conserving pseudopotentials which incorporate self-interaction corrections (SICs) we arrive at structural and electronic properties of bulk BeO which are not subject to the usual shortcomings of the standard local density approximation (LDA), most noticeably the underestimate of the band gap. The latter is particularly large for BeO amounting to more than 3 eV. It turns out that the LDA problems can largely be overcome by employing SIC pseudopotentials in DFT calculations. They cause no additional computational effort, as compared to standard LDA calculations. Our SIC approach yields a bulk band gap of 10.5 eV in excellent agreement with the measured gap of 10.6 eV and calculated structural bulk properties are found to be in very good accord with experiment, as well. Also the surface electronic structure of BeO (10 1̄ 0) shows very significant SIC-induced changes, as compared to the respective standard LDA surface band structure. For the relaxed surface, showing a bond lengths contracting rotation relaxation, we find three salient bands of surface states. Two of these occur within the fundamental gap fairly close to the projected bulk bands from which they are derived. The surface band gap resulting in SIC is 9.1 eV, as opposed to the LDA surface band gap of 6.4 eV.