Electrocatalytic carbon dioxide reduction reaction (CO₂RR) holds the promise of both overcoming the greenhouse effect and synthesizing a wealth of chemicals. Electrocatalytic CO₂ reduction toward carbon-containing products, including C₁ products (carbon monoxide, formic acid, etc), C₂ products (ethylene, ethanol, etc.) and multi-carbon products (e.g., n-propanol), provides beneficial fuel and chemicals for industrial production. The complexity of the multi-proton transfer processes and difficulties of C-C coupling in electrochemical CO₂ reduction toward multi-carbon(C₂₊) products have attracted increasing concerns on the design of catalysts in comparison with those of C₁ products. In this paper, we review the main advances in the syntheses of multi-carbon products through electrocatalytic carbon dioxide reduction in recent years, introduce the basic principles of electrocatalytic CO₂RR, and detailly elucidate two widely accepted mechanisms of C-C coupling reactions. Among abundant nanomaterials, copper-based catalysts are outstanding catalysts for the preparation of multi-carbon chemicals in electrochemical CO₂RR attributing to effective C-C coupling reactions. Regarding the different selectivity of multi-carbon chemicals but extensively applied copper-based catalysts, we classify and summarize various Cu-based catalysts through separating diverse multi-carbon products, where the modification of spatial and electronic structures is beneficial to increase the coverage of CO or lower the activation energy barrier for forming C-C bond to form the key intermediates and increase the production of multi-carbon products. Challenges and prospects involving the fundamental and development of copper-based catalysts in electrochemical CO₂ reduction reaction are also proposed.