Copper and its alloys have been in the service of humankind earlier than any other metal throughout history. In the present review, all aspects of the SPS of copper and its alloys are comprehensively investigated, and their potential effects on the microstructure and properties of alloys are thoroughly reviewed. In this regard, the densification phenomenon during SPS treatment is fully investigated. The effects of raw powder characteristics involving particle size, contamination content, and powder morphology on the sinterability of these materials are examined. Then, the influence of SPS operation parameters consisting of pressure, heating rate, dwelling time, pulsed electrical current, electrical pulses pattern, sintering temperature, and sintering tooling on densification of these materials is extensively discussed. Furthermore, the microstructure evolution and grain growth behaviors during SPS are explored. In addition, current challenges and future perspectives of this field are addressed.