Li metal has been recognized as the most promising anode materials for next-generation high-energy-density batteries, however, the inherent issues of dendrite growth and huge volume fluctuations upon Li plating/stripping normally result in fast capacity fading and safety concerns. Functionalized Cu current collectors have so far exhibited significant regulatory effects on stabilizing Li metal anodes (LMAs), and hold a great practical potential owing to their easy fabrication, low-cost and good compatibility with the existing battery technology. In this review, a comprehensive overview of Cu-based current collectors, including planar modified Cu foil, 3D architectured Cu foil and nanostructured 3D Cu substrates, for Li metal batteries is provided. Particularly, the design principles and strategies of functionalized Cu current collectors associated with their functionalities in optimizing Li plating/stripping behaviors are discussed. Finally, the critical issues where there is incomplete understanding and the future research directions of Cu current collectors in practical LMAs are also prospected. This review may shed light on the critical understanding of current collector engineering for high-energy-density Li metal batteries.