Recent publications on the mechanism of methanol synthesis on Cu-containing catalysts were critically analyzed. The following mechanisms can be distinguished based on the key intermediates: formate, carbonate, carboxyl, and formyl. A stepwise mechanism of conversion of CO2 and CO into methanol was proposed taking into account the available experimental and calculated data. According to this mechanism, hydrogenation of CO2 starts with interaction of a CO2 molecule with dissociated hydrogen chemisorbed on the copper surface, forming monodentate formate, which easily transforms into bidentate formate. Subsequent hydrogenation of bidentate formate through a series of intermediates forms methanol. Another possible route of CO2 conversion in the presence of dissociated hydrogen is formation of carboxyl, which is converted into methanol via several intermediates, including formyl. If CO is present in syngas, its role is to remove the OH groups from the surface via the surface carboxyl (*COOH). Then carboxyl can undergo the following transformations: decomposition to CO2 and H* and hydrogenation via formyl to methanol. The appearance of carbonate intermediates on the copper surface observed by IR spectroscopy at low pressures is not related to the mechanism of methanol synthesis. Some of the results of experiments obtained in the study of transition states require additional studies.