Many engineering applications require components with a good surface finish. It is difficult to get the surface finish in the micro/nano level range with conventional finishing processes for materials such as super alloys, composites, and ceramics. Magnetic abrasive finishing (MAF) is one of the processes for achieving superior surface finish. However, the processes efficiency is affected by its operational variables. Even a slight change in a processing parameter may lead to dimensional inaccuracies and poor surface quality of the workpiece. In this paper, recent trends in the magnetic abrasive finishing process are presented along with a critical review. The review includes MAF principles, tools, hybridization, modeling, and simulation of the process. Apart from plane MAF, the principle of MAF for cylindrical workpieces, the mechanism of material removal and the effect of different types of abrasives are also discussed. Various machine tools used for MAF of plane and cylindrical workpieces for external and internal surfaces are also discussed. In hybridization, different processes combined with MAF, like ultrasonic-assisted MAF, chemo-assisted MAF, and electrochemical-assisted MAF, etc., are discussed to increase material removal rate and obtain surface finish at the micro/nano level. The paper also covers mathematical and statistical modeling, simulation, and optimization techniques to predict and optimize the set of input process parameters. Lastly, challenges and conclusions of the MAF process are presented.