Magnetic abrasive finishing (MAF) has attracted much attention as an advanced nano-finishing technology in achieving high-quality surface for finishing superalloys, composites, and ceramics. This paper provides a comprehensive review on MAF process which is mainly organized by different six sections, including MAF principles, magnetic abrasive preparation, MAF tools, MAF modeling and simulation, MAF characteristics, and challenges and future directions. The principle of MAF for internal workpiece and flat workpiece is mainly introduced. Magnetic preparation methods, including simply mixing method, bonding method, sintering method, gas atomization, and rapid solidification method, are described in detail. The design of MAF tools for outer surface and inner surface is summarized. It also covers some models and simulations to predict optimal processing parameters. Force measurement and material removal mechanism to explore the MAF processes are performed. Finally, challenges and future directions are provided. This review is beneficial to researchers and practitioners in the MAF-related fields.