Oxidation catalysts are modeled by oxide single crystals, thin oxide films, as well as supported oxide nanoparticles. We characterize the surface of those materials using a variety of surface sensitive techniques including scanning tunneling microscopy and spectroscopy, photoelectron spectroscopy, infrared spectroscopy, and thermal desorption spectroscopy. We find temperature dependent structural transformations from V 2 O 5 (001) to V 2 O 3 (0001) via V 6 O 13 (001). V 2 O 3 (0001) is found to be vanadyl terminated in an oxygen ambient and it loses the vanadyl termination after electron bombardment. It is shown that the concentration of vanadyl groups controls the selectivity of the methanol oxydehydrogenation towards formaldehyde. A proposal for the mechanism is made. The results on single crystalline thin films are compared with similar measurements on deposited vanadia nanoparticles. The experimental results are correlated with theoretical calculations and models.