With the development of the aerospace and automotive industries, high heat exchange efficiency is a challenge facing the development of various industries. Pure copper has excellent mechanical and physical properties, especially high thermal conductivity and electrical conductivity. These excellent properties make pure copper the material of choice for the manufacture of heat exchangers and other electrical components. However, the traditional processing method is difficult to achieve the production of pure copper complex parts, so the production of pure copper parts through additive manufacturing has become a problem that must be overcome in industrial development. In this article, we not only reviewed the current status of research on the structural design and preparation of complex pure copper parts by researchers using selective laser melting (SLM), selective electron beam melting (SEBM) and binder jetting (BJ) in recent years, but also reviewed the forming, physical properties and mechanical aspects of pure copper parts prepared by different additive manufacturing methods. Finally, the development trend of additive manufacturing of pure copper parts is also prospected.