we study fronts of cells such as those invading a wound or in a growing tumor. first we look at a discrete stochastic model in which cells can move, proliferate, and experience cell-cell adhesion. we compare this with a coarse-grained, continuum description of this phenomenon by means of a generalized cahn-hilliard equation (gch) with a proliferation term.  there are two interesting regimes. for subcritical adhesion, there are propagating "pulled" fronts, similarly to those of fisher-kolmogorov equation. the problem of front velocity selection is examined, and our theoretical predictions are in a good agreement with a numerical solution of the gch equation. for supercritical adhesion, there is a nontrivial transient behavior. the results of continuum and discrete models are in a good agreement with each other for the different regimes we analyzed.