The band structures of some transparent conducting oxides are calculated using the screened exchange hybrid functional. The optical properties and band gaps of the CuAlO2 defossalite family follow the expected chemical trends. The limits to the doping of n- and p-type oxides are examined in terms of the dopant compensation by native defects. The accessible range of the Fermi energy under doping is that for which compensating native defects have a positive formation energy. These energy limits are aligned on a band offset diagram. N-dopable oxides have a conduction band minimum that lies deep below the vacuum level, while p-dopable oxides have a valence band top that lies high towards the vacuum level. The nature of electron conduction in amorphous InGaZnOx type oxides is discussed, in terms of the nature of localisation and the density of states at the mobility edge. (C) 2011 Elsevier B.V. All rights reserved.