The motion of domain walls is critical to many applications involving ferroelectric materials, such as fast high-density non-volatile random access memory1. In memories of this sort, storing a data bit means increasing the size of one polar region at the expense of another, and hence the movement of a domain wall separating these regions. Experimental measurements of domain growth rates in the well-established ferroelectrics PbTiO3 and BaTiO3 have been performed, but the development of new materials has been hampered by a lack of microscopic understanding of how domain walls move2, 3, 4, 5, 6, 7, 8, 9, 10, 11. Despite some success in interpreting domain-wall motion in terms of classical nucleation and growth models12, 13, 14, 15, 16, these models were formulated without insight from first-principles-based calculations, and they portray a picture of a large, triangular nucleus that leads to unrealistically large depolarization and nucleation energies5. Here we use atomistic molecular dynamics and coarse-grained Monte Carlo simulations to analyse these processes, and demonstrate that the prevailing models are incorrect. Our multi-scale simulations reproduce experimental domain growth rates in PbTiO3 and reveal small, square critical nuclei with a diffuse interface. A simple analytic model is also proposed, relating bulk polarization and gradient energies to wall nucleation and growth, and thus rationalizing all experimental rate measurements in PbTiO3 and BaTiO3.