We used ab initio simulations and calculations to study the structures and stabilities of copper oxide clusters, CunOn (n=1-8) and CuOn (n=1-6). The lowest energy structures of neutral and charged copper oxide clusters were determined using primarily the B3LYP/LANL2DZ model chemistry. In CunOn clusters with n=1-8, a transition from planar to nonplanar geometries occurs at n=4. In CuOn clusters with n=1-6, all geometries of neutral, positively, and negatively charged clusters are planar or near planar structures. Selected electronic properties, including binding energies, ionization energies, and electronic affinities, were calculated and examined as a function of n. Stabilities were examined by calculating fragmentation channels and Löwdin ...