Rare-earth metals, particularly neodymium, dysprosium, and praseodymium are becoming increasingly important in the transition to a green economy due to their essential role in permanent magnet applications such as in electric motors and generators. With the increasingly limited rare-earth supply and complexity of processing Nd, Dy, and Pr from primary ores, recycling of rare-earth based magnets has become a necessary option to manage supply and demand. Depending on the form of the starting material (sludge or scrap), there are different routes that can be used to recover neodymium from secondary sources, ranging from hydrometallurgical (based on its primary production process), electrochemical to pyrometallurgical. Pyrometallurgical routes provide solution in cases where water is scarce and generation of waste is to be limited. This paper presents a systematic review of previous studies on the high-temperature (pyrometallurgical) recovery of rare earths from magnets. The features and conditions at which the recycling processes had been studied are mapped and evaluated technically. The review also highlights the reaction mechanisms, behaviors of the rare-earth elements, and the formation of intermediate compounds in high-temperature recycling processes. Recommendations for further scientific research to enable the development of recovery of the rare-earth and magnet recycling are also presented.