For the ground state of CuO and its low-lying excited states up to Te = 30 000cm -~ potential curves, spectroscopic parameters and dissociation energies were calculated using CASSCF and MRD-CI methods. Relativistic effects were included via a no-pair Hamiltonian. By comparing observed with calculated radiative lifetimes, the experimentally observed states are assigned as follows: C2II --~ 32H, y2~+ __~ 12~+, A,2~+ -~ 22X+, A2E-~ 12~-, D2A --~ 12A or 32A. The so-called d2X -state is likely to be a quartet state contaminated by spin-orbit effects. The ground state of CuO + is predicted to be 31~-, followed by 3I"] and ~H states. The respective ionization potentials of CuO are calculated at 9-15, 10-18 and 10-60 eV. An analysis of the calculated dipole moments and d orbital occupation numbers of the various excited CuO states gives insight into the bonding characteristics of the molecule.