The cuprous oxide based ternary delafossite semiconductors have been well studied in the context of p-type transparent conducting oxides. CuAlO2, CuGaO2 and CuInO2 represent a homologous series where the electronic properties can be tuned over a large range. The optical transparency of these materials has been associated with dipole forbidden transitions, which are related to the linear O—Cu—O coordination motif. The recent demonstration that these materials can be synthesized in tetrahedral structures (wurtzite analogues of the chalcopyrite lattice) opens up a new vista of applications. We investigate the underlying structure–property relationships (for Group 3 and 13 metals), from the perspective of first-principles materials modelling, towards developing earth-abundant photoactive metal oxides. All materials studied possess indirect fundamental band gaps ranging from 1 to 2 eV, which are smaller than their delafossite counterparts, although in all cases the difference between direct and indirect band gaps is less than 0.03 eV.