We have calculated the ionization energies, electron affinities, optical excitation energies, and relaxed electron and hole states at comers, kinks, and steps of the MgO (001) surface. The calculations are performed using an embedded cluster model and density functional theory and take into account the long-range surface polarization. The extent of localization of electronic states associated with specific structural defects at the surface is studied by the participation function method. The positions of energy levels of the surface sites with respect to the top of the surface valence band and the vacuum level are determined. The results demonstrate the existence of deep and shallow electron traps at steps, comers, and kinks of the MgO (001) surface, and establish direct correlation between common surface features and their spectroscopic and other electronic properties.