Raman and infrared spectroscopy provide complementary information about the nature of the surface metal oxide species present in supported metal oxide catalysts. This paper reviews the type of fundamental information that is typically obtained in Raman and IR characterization studies of supported metal oxide catalysts. The molecular structures of the surface metal oxide species are reflected in the terminal M=O and bridging M-O-M vibrations. The location of the surface metal oxide species on the oxide supports is determined by directly monitoring the specific surface hydroxyls of the support that are being titrated. The surface coverage of the surface metal oxide species on the oxide supports can be quantitatively obtained since at monolayer coverage all the reactive surface hydroxyls are titrated and additional metal oxide results in the formation of crystalline metal oxide particles. The nature of surface Lewis and Bronsted acid sites present in supported metal oxide catalysts are determined by adsorbing basic probe molecules like pyridine. Information about the behavior of the surface metal oxide species during catalytic reactions are provided by in situ characterization studies. Such fundamental information is critical for the development of molecular structure-reactivity relationships for supported metal oxide catalysts. This paper will be limited to supported metal oxide catalysts containing group V-VII transition metal oxides (e.g., V, Nb, Cr, Mo, W and Re) on several different oxide supports (alumina, titania, zirconia, niobia and silica).