Abstract: With the global transition toward low-carbon energy systems and the growing demand for carbon emission reduction, the valorization of carbon dioxide (CO₂) and the development of renewable carbon cycles have attracted increasing attention. Methanol, as an important platform chemical and high-energy-density liquid fuel, represents a key molecular carrier for establishing an artificial carbon cycle and enabling the emerging “methanol economy”. In this context, the hydrogenation of CO/CO₂ to methanol offers a promising route for both the utilization of CO₂ from industrial emissions and the conversion of renewable carbon resources. In particular, biomass gasification can generate synthesis gas rich in CO, CO₂, and H₂, providing an attractive feedstock for coupling renewable carbon with green hydrogen to produce methanol. However, fundamental issues concerning carbon-source conversion pathways, the dynamic evolution of active sites, and long-term catalyst stability under mixed CO/CO₂ feed conditions remain unresolved. This review provides a systematic overview of the reaction mechanisms, structural engineering strategies for Cu-based catalysts, and key factors governing the catalytic performance in CO/CO₂ hydrogenation to methanol. First, the development of methanol synthesis routes based on fossil resources, renewable energy, and biomass-derived synthesis gas is reviewed, highlighting the potential of integrating mixed CO/CO₂ carbon sources with green hydrogen for sustainable methanol production. Subsequently, particular attention is devoted to the formate, carboxylate, and reverse water–gas shift (RWGS)-coupled pathways, with emphasis on the competition and interconversion among these routes and the role of interfacial structures in regulating reaction selectivity. The effects of Cu active sites, supports, promoters, and the in situ water effect on catalytic behavior are then critically discussed. Recent advances indicate that dynamic Cu–oxide interfaces, oxygen-vacancy engineering, and the construction of bifunctional active sites are central to enhancing the conversion efficiency of mixed carbon sources. Furthermore, dynamic regulation of water, stabilization of Cu nanoparticles, and multiscale interface engineering are identified as essential strategies for simultaneously achieving high activity, methanol selectivity, and long-term operational stability. Finally, in view of the increasing demand for direct methanol synthesis from biomass-derived synthesis gas, future research should focus on elucidating the dynamic evolution of active sites and controlling reaction pathways under mixed CO/CO₂ conditions. The rational design of next-generation Cu-based catalytic systems integrating CO₂ activation, CO conversion, and water management functionalities is particularly important. Such advances will provide a mechanistic foundation and technological guidance for low-carbon methanol production and sustainable carbon-cycle technologies.