Epithelial-mesenchymal plasticity (EMP) refers to the ability of cells to dynamically interconvert between epithelial (E) and mesenchymal (M) phenotypes, thus generating an array of hybrid E/M intermediates with mixed E and M features. Recent findings have demonstrated how these hybrid E/M rather than fully M cells play key roles in most of physiological and pathological processes involving EMT. To this regard, the onset of hybrid E/M state coincides with the highest stemness gene expression and is involved in differentiation of either normal and cancer stem cells. Moreover, hybrid E/M cells are responsible for wound healing and create a favorable immunosuppressive environment for tissue regeneration. Nevertheless, hybrid state is responsible of metastatic process and of the increasing of survival, apoptosis and therapy resistance in cancer cells. The present review aims to describe the main features and the emerging concepts regulating EMP and the formation of E/M hybrid intermediates by describing differences and similarities between cancer and normal hybrid stem cells. In particular, the comprehension of hybrid E/M cells biology will surely advance our understanding of their features and how they could be exploited to improve tissue regeneration and repair.