In most of the world, people have regular exposure to multiple accents. Therefore, learning to quickly process accented speech is a prerequisite to successful communication. In this paper, we examine work on the perception of accented speech across the lifespan, from early infancy to late adulthood. Unfamiliar accents initially impair linguistic processing by infants, children, younger adults, and older adults, but listeners of all ages come to adapt to accented speech. Emergent research also goes beyond these perceptual abilities, by assessing links with production and the relative contributions of linguistic knowledge and general cognitive skills. We conclude by underlining points of convergence across ages, and the gaps left to face in future work.