Abstract: The interaction between harmonics in the air-gap magnetic field of permanent magnet (PM) machines generates complex electromagnetic force wave spectra that exacerbate vibration, limiting their widespread application in high-end equipment such as aerospace and naval propulsion systems. Investigating the generation mechanisms and suppression methods of PM machine electromagnetic vibration is crucial for ensuring highly reliable operation. This paper qualitatively analyzes electromagnetic force waves and structural modes in PM machines, while summarizing calculation methods for electromagnetic force waves, stator natural frequencies, and multi-factor-influenced electromagnetic vibration. Current research on PM machine vibration suppression is reviewed, covering electromagnetic structure improvements (including permanent magnets, stator/rotor components, and armature windings) and drive control enhancement methods. Additionally, the paper examines rotor eccentricity and bearing clearance effects on electromagnetic vibration, as well as vibration impacts on mechanical systems within electromechanical coupling systems. Finally, future research directions for PM machine electromagnetic vibration are outlined.