Eccentricity fault with 10% severity is probably the only existing fault in a brand new healthy electrical machine that is acceptable as a manufacturing tolerance. This fault can be developed due to a continuous pull between stator and rotor, even in a de-energized machine. So, it must be diagnosed,and its severity monitored. The authors introduced and criticized various indices for eccentricity fault diagnosis. Advantages, drawbacks, and ambiguous points of each index and potential ground for improvement of these techniques are addressed. Moreover, different eccentric PM machine modelling techniques are reviewed and environmental factors affecting the eccentricity fault detection process are discussed. This survey covers all direct current and alternating current PM machines. It provides information about the researches performed since 1986 and it is helpful to newcomers to this field, artisans, and protection system designers. Considering the given information, the readers achieve enough understanding of the weaknesses and strong points of each eccentricity fault diagnosis index. Then, these indices are evaluated through assigning weight coefficients under various scenarios. Interested individuals can modify these weight coefficients based on the specifics of the application and decide which index is the most appropriate.