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Grain boundaries in polycrystalline materials migrate to reduce the total excess energy. It has recently been found that the factors governing migration rates of boundaries in bicrystals are insufficient to explain boundary migration in polycrystals. We first review our current understanding of the atomistic mechanisms of grain boundary migration based on simulations and high-resolution transmission electron microscopy observations. We then review our current understanding at the continuum scale based on simulations and observations using high-energy diffraction microscopy. We conclude that detailed comparisons of experimental observations with atomistic simulations of migration in polycrystals (rather than bicrystals) are required to better understand the mechanisms of grain boundary migration, that the driving force for grain boundary migration in polycrystals must include factors other than curvature, and that current simulations of grain growth are insufficient for reproducing experimental observations, possibly because of an inadequate representation of the driving force.