The electronic structure of oxides with the perovskite and cadmium halide structures are derived using tight-binding theory and the angular overlap model. The control of the form of the energy bands by the presence of vertex- (perovskite) and edge-sharing (cadmium halide) of the coordination octahedra is first explored using one-dimensional examples. For one-, two-, and three-dimensional structures of the perovskite type, a very interesting result is uncovered. It is shown that on the band model a band gap may only arise if the oxygen 2s orbital is included in the orbital problem. Prediction of the magnitude of the band gaps in d(6) perovskites is thus not a simple matter. This band structure, derived from tight-binding theory via the construction of Bloch orbitals, is compared with an energy band scheme based on local crystal field orbitals and covalent metal-oxygen interactions, which has traditionally been used in this area.