Copper has been widely used in many applications due to its outstanding properties such as malleability, high corrosion resistance, and excellent electrical and thermal conductivities. While 3D printing can offer many advantages from layer-by-layer fabrication, the 3D printing of highly pure copper is still challenging due to the thermal issues caused by copper’s high conductivity. This paper presents a comprehensive review of recent work on 3D printing technology of highly pure copper over the past few years. The advantages and current issues of 3D printing methods are compared while different properties of copper parts printed by these methods are summarized. Finally, we provide several potential applications of the 3D printed copper parts and an overview of current developments that could lead to new improvements in this advanced manufacturing field.