The bulk and surface properties of Cu2O were studied theoretically at the density-functional level (DFT). The calculated structural parameters, binding energy per Cu2O molecule (Eu) and electronic properties were compared with available experimental bulk data. The convergence of the surface energy was investigated for both non-polar (oxygen terminated) and polar (copper terminated) (1 1 1) surfaces. The electronic properties of both surfaces showed that there are surface states both at the top of the valence band and the bottom of the conduction band, indicating strong surface excitons decreasing the band gap. The structural relaxation was investigated for both cases. The study shows that the stoichiometric O-terminated Cu2O(1 1 1) surface exhibits minor relaxation, whereas the Cu-terminated surface undergoes extensive relaxation minimizing the surface polarity and indicative of surface reconstruction for this termination.