The abrasive flow finishing processes are advanced finishing techniques widely used as finishing solutions in high-end industries like aerospace, automobile, tool and die, and prosthetic. Abrasive flow finishing processes are mainly used for polishing, deburring, removal of cast layers, radiusing and finishing intricate shapes by flowing abrasive laden viscoelastic carrier over the surfaces to be finished. Although abrasive flow finishing have a wide range of applications and could be used in every shop floor as a finishing solution, their usage is limited owing to high initial and running costs associated with them. This article attempts to present a novel classification of abrasive flow finishing processes based upon the use of different energy and tooling, and highlights the critical research outcomes in each category. The physical abrasive flow finishing modeling, developments in abrasive flow finishing processes, and their hybridization with the other manufacturing processes are discussed. Finally, the future research challenges including the development of low-cost alternative media, development of tooling and fixture, and environmental issues in the area of abrasive flow finishing are highlighted.