Additive manufacturing is an emerging technique for manufacturing complex shapes rather than traditional manufacturing procedures due to the tool free manufacturing method. The complex components manufactured by this technique have a high surface roughness, which reduces fatigue strength, influences the wear of mating components, reduces the cooling efficiency of complex cooling channels, and so on. The surface roughness of complex cooling channels, for example, affects the formation of boundary layers, partial liquid flow, and heat transfer coefficients. As a result, the finishing processes are required for additively manufactured components to reduce the surface roughness. Chemical based finishing processes for additively manufactured parts have been developed by the researchers because it is a noncontact and automatic finishing process. However, a lack of understanding of the fundamental mechanisms governing these finishing processes may limit their practical uses in areas like aerospace, automobiles, and defense. In this review study, the mechanisms of various chemical and electrochemical based finishing processes are explained first, followed by the current state of the finishing processes of additively manufactured components. Surface integrity, for example, is controlled by experimental factors that are revealed first, followed by various researchers choosing acceptable input parameters to achieve the low surface roughness. In addition, this article provides future perspectives on finishing processes and a view into the process selection based on the component complexity and cost.