The compounds InMO4 (M=V, Nb, Ta) and BiVO4 are promising photocatalysts which are able to induce hydrolysis of water molecules under visible light irradiation. By first principles calculations, supported by experiments, we inspect their peculiar electronic structure in an attempt to rationalize the link between the bulk crystal architecture of the materials and the related electronic properties. We find that the bottom of the conduction band of InMO4 systems consists of a large contribution (about 20%) due to 5s orbitals of In atoms. Another dominant component comes from d orbitals of V, Nb, and Ta. On the other hand, the top of the valence band of the BiVO4 shows a contribution from 6s orbitals of Bi of about 18% as well as a dominant component due to 2p states of O. We can infer that the photocatalytic activity could be improved by the large mobility coming from the s orbital component as well as by tuning the electron affinity (position of the bottom of the conduction band) and ionization potential (top of the valence band). The absorption process of a H2O molecule in the InVO4 system was studied by fully relaxing the structure via first principles calculations. Our simulations have shown that the lone pairs of the O atom belonging to the H2O molecule have a strong tendency to bind to In, while, at the same time, at least one of the H atoms of the water molecule forms a hydrogen bond with the O of the InVO4 catalyst surface. When a water molecule absorption occurs, it induces a shortening of the In-In and In-V bond lengths around at the surface layer. This might suggest that the electron mobility is locally enhanced due to the resulting larger orbital overlap of In_5s-In_5s and In_5s-V_3d with respect to the case of absence of water.