In this paper, we present the results of electronic structure, ab initio calculations performed on ReO3, WO3, and the stoichiometric tungsten bronze NaWO3. We examine the relation between the structural and the electronic properties of the three materials and comment on the solid state chemistry governing the interaction between the transition metal and its oxygen ligands. We show that off-center displacements of the W ion in WO3 are driven by the onset of covalent interactions with the nearest oxygen, while the metallic materials ReO3 and NaWO3 are stable when cubic. In the latter case, antibonding contributions due to the occupation of the conduction band oppose the deformation. The different behavior is justified by examining the band structure of the compounds. The effect of the different number of valence electrons and of the different nature of the transition metal on the electronic distribution in the solid are analyzed. Finally, by comparing the mechanical properties of the three oxides, we show that the antibonding conduction electron makes ReO3 very rigid and can suggest an explanation for the pressure-induced phase transition observed for this material.