Induction machines are widely used in different applications. Unpredicted breakdown of these machines usually leads to costly downtime and repairs. These expenses can be minimized by using proper condition monitoring techniques. Eccentricity fault is one of the widespread faults causing machine malfunction; its detection could be useful for preventing of harmful consequences. In this paper, different works on eccentricity fault diagnosis of induction machines with different types of supply have been reviewed. Due to extensive use of induction machines in wind turbines (WT) as doubly-fed induction generator (DFIG), in addition to declaration of importance of eccentricity fault diagnosis in DFIG, detection of eccentricity fault in DFIG is also reviewed.