The interfacial tension between two cell subpopulations in direct contact represents a key physical parameter responsible for the self-organization of tissues during biological processes such as morphogenesis and the spreading of cancers. Higher interfacial tension (i) reduces the spreading of cancer-mesenchymal cells through the epithelial subpopulation, (ii) ensures efficient cell segregation in co-cultured systems, (iii) can induce extrusion of cancer-mesenchymal cells along the biointerface with the epithelial subpopulation, and (iv) results in the generation of higher mechanical stress along the biointerface. Inhomogeneous distribution of the interfacial tension leads to the Marangoni effect, which further facilitates the rearrangement of cells. The formation of mobile stiffness gradients, known as durotaxis, under in vivo conditions is directly related to an inhomogeneous distribution of the interfacial tension. As the product of homotypic and heterotypic cell–cell interactions, the interfacial tension depends on the distance between the subpopulations, which varies over time. This review (i) summarizes biological aspects related to the homotypic and heterotypic cell–cell interactions along the biointerface, together with the viscoelasticity of cell subpopulations caused by collective cell migration and by compression (de-wetting)/extension (wetting) of the subpopulations; and (ii) describes these same biological aspects from a biophysical/ mathematical perspective by pointing to the role played by the interfacial tension.