The band structures of cubic Cu{sub 2}O and monoclinic CuO crystals have been calculated by means of the first-principles orthogonalized linear combination of atomic orbitals method. Using the wave functions obtained, the frequency-dependent interband optical conductivities are also evaluated. The results show Cu{sub 2}O to be a direct-gap semiconductor, while CuO is semiconductorlike with an intrinsic hole population at the top of the valence band (VB). By comparing with a variety of existing data, we conclude that band theory works extremely well for Cu{sub 2}O, but is less satisfactory for CuO. This could be due to strong correlation effects for states near the top of the VB in CuO. A careful reanalysis of optical data and excitonic spectra in Cu{sub 2}O in conjunction with our calculations suggests a complete reinterpretation of these data. A clear distinction between the intrinsic gap and the optical gap is argued. We conclude that the intrinsic gap in Cu{sub 2}O is of the order of 0.8 eV, while the optical gap is of the order 2.0--2.3 eV. The excitonic series in Cu{sub 2}O is due to the Coulombic attraction of the hole at the top of the VB and the electron in the next-higher conductionmore » band (CB), not the lowest CB, because of the forbidden symmetry associated with angular-momentum conservation. This reinterpretation of the excitonic data is also consistent with a calculated low value for the static dielectric constant {epsilon}{sub 0} of order of 4 for Cu{sub 2}O.« less