Since the 1960s, extensive studies have been made on rare earth (RE) - transition metal (TM) alloys due to their excellent functional properties. Most of functional properties of these alloys including magnetic properties are closely related to the 4f electrons of RE elements. The use of RE-TM alloys has increased significantly in a number of industrial fields over the past few decades. In particular, the demand for Dy-added Nd-Fe-B magnets is rapidly increasing because these magnets are indispensable for high-performance motors in electric vehicles and hybrid electric vehicles. These magnets need to possess sufficient thermal stability for use in such motors in high-temperature environments. The addition of Dy is necessary to improve the thermal stability of Nd-Fe-B magnets. However, Dy resources are scarce and unevenly located in the earth crust. Thus, it is necessary to develop an inexpensive and effective recovery/separation process of Dy from scraps of the Dy-added Nd-Fe-B magnet. In this review paper, one of the practical refining process, molten salt electrolysis, of rare earth elements such as Dy and Nd is described. Moreover, new recovery/separation process of Dy and Nd from Nd magnet scraps proposed by our group is introduced.