Abstract: Copper and its alloys possess excellent thermal conductivity, electrical conductivity and processing performance, and are widely applied in aerospace, electronic and electrical, and mechanical manufacturing fields. However, traditional processing techniques struggle to achieve the integrated manufacturing of copper components with both complex and precise geometries and high performance requirements. Laser powder bed fusion (LPBF), as an advanced additive manufacturing technology, offers a new approach for the precise forming of copper components; yet, the inherent properties of copper, such as its susceptibility to oxidation, high reflectivity, high thermal conductivity and high melting point, can lead to defects such as melt pool instability, porosity and stress deformation during the LPBF process, severely restricting the forming quality and application promotion. This paper reviews the technical principles and typical defect types of LPBF, focuses on analyzing the key issues and existing solutions for copper and its alloys in LPBF processing, and systematically summarizes the research progress in recent years on the use of green laser in the preparation of pure copper, CuCrZr and CuCrNb alloys from the aspects of forming process, microstructure control and performance improvement. Based on the practical accumulation of our team in the green laser LPBF forming of pure copper and its alloys, the technical advantages and development potential of short-wavelength lasers such as green laser in the high-quality forming of high-reflectivity materials are clarified. In addition, the future development trends of laser additive manufacturing of copper and its alloys are prospected from three cutting-edge directions: real-time process monitoring and feedback, beam shaping, and large-area multi-beam multi-material composite manufacturing, to provide theoretical references and technical guidance for scientific research innovation and engineering application in this field.