In the hydrogenation of CO2, the product distribution is mainly affected by the interaction between oxide supports and Cu, the active sites for CO2 activation, surface reaction mechanism, and surface reaction pathway, where the microstructure of the metal-support interface is important. This paper summarized the progress in the Cu-based catalyst supports for methanol synthesis from CO2, and the emphasis was placed on ZnO, ZrO2, CeO2, and TiO2 which possess oxide vacancies during the reaction. Then the supports effects of SiO2, Al2O3, Zn-Zr, Ce-Zr, and perovskite were briefly introduced. The Cu/ZnOx interface formed by strong metal-support interaction(SMSI) is the main active site for CO2 hydrogenation, and its microstructure and reaction mechanism have been extensively investigated. The researches on Cu/ZrO2 have been focused on the crystalline phase of ZrO2, but there remains debate in the conclusions. The reaction mechanism study of Cu/CeO2 is still limited to the reverse CeO2/Cu(111) model and the morphology of CeO2 affects the interaction between Cu and the supports, and hence affects the product distribution. There are a variety of factors such as crystalline phase and facet that affect the catalytic properties of Cu/TiO2 but the current research is not complete. Finally, this paper outlined the research should be conducted in future, i.e. The obverse model surface which are consistent with the real catalyst surface is used for fundamental research and the structural changes of the catalysts during reaction are explored via in-situ characterization so that the efficient and low-cost Cu based catalyst supported on multicomponent oxide can be ultimately designed. © 2020, Chemical Industry Press. All right reserved.