Not all cells undergo a complete EMT, i.e. losing their cell-cell adhesion and gaining solitary migration characteristics. Instead, most cells undergo partial EMT, a state in which they retain some epithelial traits such as cell-cell adhesion or apico-basal polarity, and gain migratory traits, thus cells in this hybrid epithelial/mesenchymal (E/M) phenotype are endowed with special properties such as collective cell migration. Single-cell tracking contributes to enabling the visualization of morphological transitions during EMT, the discernment of cell migration phenotypes, and the correlation of the heritability of these traits among sister cells. Two mathematical models have been proposed, attempting to explain the emergence of this hybrid E/M phenotype, and its highly likely that different cell lines adopt different hybrid state(s), as shown by experiments in MCF10A, HMLE and H1975 cell lines. Although a hybrid E/M state has been referred to as metastable or transient, recent experiments in H1975 cells suggest that this state can be stably maintained by cells.