Rare-earth permanent magnets (RE-PMs) are widely used in high-efficiency and high-torque density electrical machines. However, in recent years, the exclusive and unstable supply of rare-earth elements (REEs) is a major concern to substitute RE-based electrical machines by less or even no RE alternatives. Ferrite (Fe) PMs as the least expensive PMs show promising opportunities for designing low-cost non-RE electrical machines. This article reviews some relevant works on Fe-based machines, which generally have been conducted to replace RE-based machines. Fe-based machines, including PM brushless, PM-assisted synchronous reluctance, PM flux switching, and PM Vernier machines, are introduced and their main design challenges, such as low PM energy product and vulnerability to irreversible demagnetization, are addressed. In addition, a comparison of RE- and Fe-based machines reveals that when both cost and efficiency are the major concerns, Fe-based machines can be a good successor to RE-based machines. © 2020 IEEE.