Molecular vanadia species supported on the surface of metal oxides are used as catalysts for many hydrocarbon oxidation reactions. This paper discusses (i) the structure of the surface vanadia species in fresh and dehydrated catalysts, (ii) the structural and oxidation state changes during C4 hydrocarbon oxidation, and (iii) the roles of the oxide support, the surface oxygen species, and the acidity of the supported vanadia catalysts in selective oxidation catalysis, The molecular structure and reactivity information provides new fundamental insights into the catalytic properties of surface vanadia species during C4 hydrocarbon oxidation. On the other hand, the studies of the model supported vanadia catalysts shed new light on the origins of the catalytic activity of the bulk vanadium-phosphorus oxide (VPO) catalysts for partial oxidation of rt-butane to maleic anhydride. The new fundamental structure-activity and selectivity relationships of surface vanadia species on oxide supports provide a foundation for the molecular engineering of supported catalysts for selective oxidation of hydrocarbons.