Density functional approaches have become well known in applications of equilibrium statistical mechanics to phase diagrams, interfacial structures, and free energies. This paper describes how these methods can be extended to the dynamics of phase transitions. Two aspects are emphasized: the calculation of free-energy barriers in nucleation and of growth velocities for crystallization from the melt. Significant deviations from classical nucleation theory and from diffusion-based theories of crystal growth are found. The continuum density functional approach is effective in describing the dynamics of collective-mode fluctuations, which dominate single-particle dynamics in these cases. The role of body-centred ordering at the interface between a face-centred crystal and the melt is described.