  We discuss several continuum cell-cell adhesion models based on the
underlying microscopic assumptions. We propose an improvement on these models
leading to sharp fronts and intermingling invasion fronts between different
cell type populations. The model is based on basic principles of localized
repulsion and nonlocal attraction due to adhesion forces at the microscopic
level. The new model is able to capture both qualitatively and quantitatively
experiments by Katsunuma et al. (2016) [J. Cell Biol. 212(5), pp. 561--575]. We
also review some of the applications of these models in other areas of tissue
growth in developmental biology. We finally explore the resulting qualitative
behavior due to cell-cell repulsion.
