The photoelectron spectroscopy of NO3 is of considerable interest, particularly because of the radical's relevance in atmospheric chemistry, but recent studies gave controversial results. In the current study we present high-level ab initio calculations of the vertical and adiabatic electronic spectrum of NO3+ and the photoelectron spectrum of the radical. The vertical ionization spectrum up to 18 eV was calculated by complete active space self-consistent field and multireference configuration interaction methods, using extended basis sets. For D-3h geometries 15 ionic singlet and triplet states are found and characterized within this energy range, of which only the lowest four are due to principal ionization. For geometries of lower symmetry these states split into 23 states, of which seven correspond to principal ionizations. Equilibrium geometries and harmonic frequencies were computed for the controversial higher principal ionizations, and adiabatic ionization potentials were obtained. These results disagree in several points with previous experiments and their interpretation, which is discussed in detail.