Adsorption and desorption of methanol on the (111) and (100) surfaces of  Cu2O have been studied using high-resolution photoelectron spectroscopy in the temperature range 120–620 K, in combination with density functional theorycalculations and sum frequency generation spectroscopy. The bare (100) surfaceexhibits a (3,0; 1,1) reconstruction but restructures during the adsorption process into a Cu-dimer geometry stabilized by methoxy and hydrogen binding in Cu-bridge sites. During the restructuring process, oxygen atoms from the bulk that can host hydrogen appear on the surface. Heating transforms methoxy to formaldehyde, but further dehydrogenation is limited by the stability of the surface and the limited access to surface oxygen. The (√3 × √3)R30°-reconstructed (111) surface is based on ordered surface oxygen and copper ions and vacancies, which offers a palette of adsorption and reaction sites. Already at 140 K, a mixed layer of methoxy, formaldehyde, and CHxOy is formed. Heating to room temperature leaves OCH and CHx. Thus both CH-bond breaking and CO-scission are active on this  surface at low temperature. The higher ability to dehydrogenate methanol on (111) compared to (100) is explained by the multitude of adsorption sites and, in particular, the availability of surfaceoxygen.