  Collective cell migration is a key driver of embryonic development, wound
healing, and some types of cancer invasion. Here we provide a physical
perspective of the mechanisms underlying collective cell migration. We begin
with a catalogue of the cell-cell and cell-substrate interactions that govern
cell migration, which we classify into positional and orientational
interactions. We then review the physical models that have been developed to
explain how these interactions give rise to collective cellular movement. These
models span the sub-cellular to the supracellular scales, and they include
lattice models, phase fields models, active network models, particle models,
and continuum models. For each type of model, we discuss its formulation, its
limitations, and the main emergent phenomena that it has successfully
explained. These phenomena include flocking and fluid-solid transitions, as
well as wetting, fingering, and mechanical waves in spreading epithelial
monolayers. We close by outlining remaining challenges and future directions in
the physics of collective cell migration.
