With the rapid development of high-end manufacturing industries such as aerospace and national defense, the demand for metal additive manufactured parts with complex internal cavities has been steadily increasing. However, the finishing of complex internal surfaces, especially for irregularly shaped parts, remains a significant challenge due to their intricate geometries. Through a comparative analysis of common finishing methods, the distinctive characteristics and applicability of magnetic abrasive finishing (MAF) are highlighted. To meet the finishing needs of complex metal additive manufactured parts, this paper reviews the current research on magnetic abrasive finishing devices, processing mechanisms, the development of magnetic abrasives, and the MAF processes for intricate internal cavities. Future development trends in MAF for complex internal cavities in additive manufactured parts are also explored; these are (1) investigating multi-technology composite magnetic abrasive finishing equipment designed for complex internal surfaces; (2) studying the dynamic behavior of multiple magnetic abrasive particles in complex cavities and their material removal mechanisms; (3) developing high-performance magnetic abrasives suitable for demanding conditions; and (4) exploring the MAF process for intricate internal surfaces.