With the advent of high-flux density permanent magnets based on rare earth elements such as neodymium (Nd) in the 1980s, permanent magnet-based electric machines had a clear performance and cost advantage over induction machines when weight and size were factors such as in hybrid electric vehicles and wind turbines. However, the advantages of the permanent magnet-based electric machines may be overshadowed by supply constraints and high prices of their key constituents, rare earth elements, which have seen nearly a 10-fold increase in price in the last 5 years and the imposition of export limits by the major producing country, China, since 2010. We outline the challenges, prospects, and pitfalls for several potential alloys that could replace Nd-based permanent magnets with more abundant and less strategically important elements.