The rare-earths criticality issue in the permanent magnet-related industries, which symbolically manifested itself in a sudden inflation of prices of rare-earth oxides and alloys starting in 2011 and ceasing in 2012, includes the general issues concerning the rare-earth resources and/or supply risks caused by rapid increase in market demands coupled with increasing environmental regulations on mining or smelting operations in supplier countries. Thus, R&D efforts for development of permanent magnets that do not use or significantly reduce the usage of the rare-earth metals have existed for more than a decade. The efforts have yielded significant developments in novel permanent magnets and the underlining materials science, and their importance is further increasing under the current geopolitical environments. In this chapter, this issue is briefly overviewed.