CuWO4 is a semiconducting oxide with interesting applications in photocatalysis. In this paper we present an accurate study of the electronic properties of stoichiometric and oxygen deficient CuWO4 based on a dielectric dependent hybrid density functional. In CuWO4 the Cu ions (Cu2+) are in a 3d9 configuration, so that the material must be classified as a magnetic insulator. Various magnetic configurations of CuWO4 have been considered, the most stable configuration being anti-ferromagnetic. The band structure, described in terms of density of states (DOS), exhibit the presence of a wide band dominated by W 5d states, separated by about 5 eV from the top of the valence band (VB), consisting of O 2p states partly mixed with Cu 3d states. The empty component of the Cu 3d orbitals forms a narrow band 3.6 eV above the VB maximum. The electronic structure emerging from the DOS curves and the Kohn-Sham energies is hard to reconcile with an experimental band gap of 2.1-2.3 eV. This gap can be rationalized within the Mott-Hubbard model of magnetic insulators, and has been computed from the total energies of the system with one electron removed from the O 2p band and one electron added to the Cu 3d states. Computing the charge transition levels for CuWO4, we come to a theoretical band gap of 2.1 eV, in excellent agreement with the experimental observations. We also studied the nature of the oxygen vacancy in CuWO4 with particular attention to the electron redistribution following the oxygen removal. The excess electrons, in fact, can occupy the localized 3d states of Cu or the localized 5d states of W. The resulting solution depends on various factors, including the concentration of oxygen vacancies.