The chemical reduction of carbon dioxide (CO 2 ) has always drawn intensive attention as it can not only remove CO 2 which is the primary greenhouse gas but also produce useful fuels. Industrial synthesis of methanol utilizing copper-based catalysts is a commonly used process for CO 2 hydrogenation. Despite extensive efforts on improving its reaction mechanism by identifying the active sites and optimizing the operating temperature and pressure, it is still remains completely unveiled. The selectivities of CO 2 electroreduction at copper electrode could mainly be towards carbon monoxide (CO), formic acid (HCOOH), methane (CH 4 ) or ethylene (C 2 H 4 ), which depends on the chemical potentials of hydrogen controlled by the applied potential. Interestingly, methanol could hardly be produced electrochemically despite utilizing metallic copper as catalysts in both processes. Moreover, the mechanistic researches have also been performed aiming to achieve the higher selectivity towards more desirable higher hydrocarbons. In this work, we review the present proposals of reaction mechanisms of copper catalyzing CO 2 reduction in industrial methanol synthesis and electrochemical environment in terms of density functional theory (DFT) calculations, respectively. In addition, the influences of the simulation methods of solvation and electrochemical model at liquid-solid interface on the selectivity are discussed and compared. methanol synthesis, electrocatalytic reduction of CO 2 , CO 2 hydrogenation, selectivity