Magnetically assisted abrasive finishing (MAAF) processes are the precision material removal processes that have been applied to a large variety of materials from brittle to ductile and from magnetic to non magnetic. The MAAF process relies on a unique “smart fluid”, known as Magnetorheological (MR) fluid. MR fluids are suspensions of micron sized magnetizable particles such as carbonyl iron, dispersed in a non-magnetic carrier medium like silicone oil, mineral oil or water. The MAAF processes overcome the limitation of abrasive flow machining by deterministically control the abrading forces by applying magnetic field around the workpiece. MAAF process is divided into two parts; one is magnetorheological finishing (MRF) and another is magnetorheological abrasive flow finishing (MRAFF). The MRAFF process gives better results as compared to results of MRF because it has additional reciprocating motion of MR fluid. In this article the attempt has been made to review various technical papers related to MRF and MRAFF. The experimental setups, process parameters, MR fluid, modeling & optimization and applications are discussed in this paper. This review article will be useful to academicians, researchers and practitioners as it comprises significant knowledge pertaining to MAAF.