Epithelial-mesenchymal transitions (EMTs) drive epithelial remodelling by converting cohesive, stable epithelial layers into individual, motile mesenchymal cells. It is now becoming clear that, from being an all-or-nothing switch, EMT can be applied in a fine-tuned manner to allow the efficient migration of cohesive epithelia that maintain their internal organisation. Recent work suggests that such collective motility involves a complex balance between epithelial and mesenchyme-like cell states that is driven by internal and external cues. Although this cohesive mode requires more complex control than single cell migration, it creates opportunities in term of tissue guidance and shaping that are starting to be unravelled.