Research on the modeling and fault diagnosis of rotor eccentricities has been conducted during the past two decades. A variety of diagnostic theories and methods have been proposed based on different mechanisms, and there are reviews following either one type of electric machines or one type of eccentricity. Nonetheless, the research routes of modeling and diagnosis are common, regardless of machine or eccentricity types. This article tends to review all the possible modeling and diagnostic approaches for all common types of electric machines with eccentricities and provide suggestions on future research roadmap. The paper indicates that a reliable low-cost non-intrusive real-time online visualized diagnostic method is the trend. Observer-based diagnostic strategies are thought promising for the continued research.