A large family of bifunctional 1,2,4-triazole molecular tectons (tr) has been explored for engineering molybdenum(VI) oxide hybrid solids. Specifically, tr ligands bearing auxiliary basic or acidic groups were of the type amine, pyrazole, 1H-tetrazole, and 1,2,4-triazole. The organically templated molybdenum(VI) oxide solids with the general compositions [MoO3(tr)], [Mo2O6(tr)], and [Mo2O6(tr)(H2O)(2)] were prepared under mild hydrothermal conditions or by refluxing in water. Their crystal structures consist of zigzag chains, ribbons, or helixes of alternating cis-{MoO4N2} or {MoO5N} polyhedra stapled by short [N-N]-tr bridges that for bitriazole ligands convert the motifs into 2D or 3D frameworks. The high thermal (235-350 degrees C) and chemical stability observed for the materials makes them promising for catalytic applications. The molybdenum(VI) oxide hybrids were successfully explored as versatile oxidation catalysts with tert-butyl hydroperoxide (TBHP) or aqueous H2O2 as an oxygen source, at 70 degrees C. Catalytic performances were influenced by the different acidic basic properties and steric hindrances of coordinating organic ligands as well as the structural dimensionality of the hybrid.