Copper pollution of the world’s water resources is becoming increasingly serious and poses a serious threat to human health and aquatic ecosystems. With reported copper concentrations in wastewater ranging from approximately 2.5 mg/L to 10,000 mg/L, a summary of remediation techniques for different contamination scenarios is essential. Therefore, it is important to develop low-cost, feasible, and sustainable wastewater removal technologies. Various methods for the removal of heavy metals from wastewater have been extensively studied in recent years. This paper reviews the current methods used to treat Cu(II)-containing wastewater and evaluates these technologies and their health effects. These technologies include membrane separation, ion exchange, chemical precipitation, electrochemistry, adsorption, and biotechnology. Thus, in this paper, we review the efforts and technological advances made so far in the pursuit of more efficient removal and recovery of Cu(II) from industrial wastewater and compare the advantages and disadvantages of each technology in terms of research prospects, technical bottlenecks, and application scenarios. Meanwhile, this study points out that achieving low health risk effluent through technology coupling is the focus of future research.