Soft electronics that can simultaneously offer electronic functions and the capability to be deformed into arbitrary shapes are becoming increasingly important for wearable and bio-implanted applications. The past decade has witnessed tremendous progress in this field with a myriad of achievements in the preparation of soft electronic conductors, semiconductors, and dielectrics. Among these materials, copper-based soft electronic materials have attracted considerable attention for their use in flexible or stretchable electrodes or interconnecting circuits due to their low cost and abundance with excellent optical, electrical and mechanical properties. In this review, we summarize the recent progress on these materials with the detailed discussions of the synthesis of copper nanomaterials, approaches for their assemblies, strategies to resist the ambient corrosion, and their applications in various fields including flexible electrodes, sensors, and other soft devices. We conclude our discussions with perspectives on the remaining challenges to make copper soft conductors available for more widespread applications.