Density functional methods are applied to explore the reaction mechanism for CO2 hydrogenation to methanol over low-index Cu surfaces, namely Cu(110) and Cu(100). A detailed reaction network is obtained, examining several different possible mechanistic routes, including methanol formation via formate and hydrocarboxyl bound intermediates, the role of formaldehyde and formic acid as stable intermediary reaction products, as well as exploring the possibility of CO2 dissociation and subsequent hydrogenation of the resultant CO. We find that, in contrast to the dominant Cu(111) facet, the Cu(110) and Cu(100) surfaces facilitate a moderate extent of CO2 activation, which results in lower activation barriers for initial elementary processes involving CO2 hydrogenation and dissociation, opening up reaction pathways considered unfeasible for Cu(111). Consequently, a wider variety of potential mechanistic routes to achieve methanol synthesis is observed and compared to Cu(111), illustrating the essential role of the Cu surface structure in catalytic activity, and providing insights into the mechanism of CO2 hydrogenation over Cu-based catalysts. In providing a thorough and detailed exploration of all of the possible mechanistic pathways for CO2 conversion to methanol, the present work represents a reference point for future studies investigating systems representative of the industrial Cu/ZnO catalyst, enabling a clear identification of the limitations of unsupported Cu catalysts, and thus allowing a more complete understanding of the role of the support material.