Abstract: After the climate shift, ENSO events could be classified into two different types. These two types of ENSO events exert quite different influence on the global climate. Earlier studies mostly classified ENSO events qualitatively, while the recent studies started to classify ENSO events quantitatively through mathematical methods like Empirical Orthogonal Function and Singular Value Decomposition. They obtained EOF modes that could describe different types of ENSO events and then defined indices that could classify ENSO events. The progress of the investigation on the classification of two types of ENSO events is summarized, and also a comparison of classification abilities among different index groups is made.