This chapter focuses on “rare earth permanent magnets”. The REPM are metal magnets. Their magnetically active components are alloys of one or more of the 3d-transition metals (abbreviated TM or T) with elements of the rare earth group (symbols RE or R). The rare earths comprise the fifteen 4f-elements, La through Lu, and Y. Of these, some that are mentioned in the chapter are of particular significance for magnets in combination with cobalt as the main alloying component. The chapter presents two major subgroups of REPM: the rare earth-cobalt magnets, most commonly based on Sm-Co alloys, and the RE-Fe-based magnets typefied by Nd-Fe-B, and discusses the rare earth-cobalt (RE-Co) permanent magnets with a fairly applied bias. Alloy of samarium with cobalt (or with Co and Fe) are technologically the most important. The chapter discusses the fundamentals of rare earth-cobalt magnets, magnet manufacturing technology, properties of commercial magnets, and applications of the REPMs.