Regarding the restrictions recently imposed by China on the export of rare-earth elements (REEs), the world may face a serious challenge in supplying some REEs such as neodymium and dysprosium soon. Recycling secondary sources is strongly recommended to mitigate the supply risk of REEs. Hydrogen processing of magnetic scrap (HPMS) as one of the best approaches for magnet-to-magnet recycling is thoroughly reviewed in this study in terms of parameters and properties. The processes of hydrogen decrepitation (HD) and hydrogenation–disproportionation–desorption–recombination (HDDR) are two common methods for HPMS. Employing a hydrogenation process can shorten the production route of new magnets from the discarded magnets compared to other recycling routes such as the hydrometallurgical route. However, determining the optimal pressure and temperature for the process is challenging due to the sensitivity to the initial chemical composition and the interaction of temperature and pressure. Pressure, temperature, initial chemical composition, gas flow rate, particle size distribution, grain size, and oxygen content are the effective parameters for the final magnetic properties. All these influencing parameters are discussed in detail in this review. The recovery rate of magnetic properties has been the concern of most research in this field and can be achieved up to 90% by employing a low hydrogenation temperature and pressure and using additives such as REE hydrides after hydrogenation and before sintering.