Metal additive manufacturing (AM) is applied in the fields of aerospace, medical implantation, etc. with booming prospects. However, the as-built surfaces of AM metal parts are not qualified for high performance requirements without post-processing due to the poor quality. At present, polishing is one of the key technologies in high performance AM technical process chains. The current applications of AM metal parts, the inherent characteristics of staircase effect, balling effect and powder adhesion in building process, and the surface morphologies like high roughness of formed surfaces were summarized. On this basis, advances in polishing technologies of AM metal parts, i.e. electrochemical polishing, laser polishing, and abrasive flow machining, were reviewed. Based on the AM samples produced by different manufacturing technologies, different metal powder materials and different structural forms (porous structure, flow channel with high aspect ratio, etc.), the polishing research results of AM metal parts were summarized through technical indexes such as surface roughness, material removal, surface residual stress, profile accuracy retention, etc. Finally, the development direction of polishing technology for AM metal parts was prospected.