We derive the phenomenological dynamics of interfaces from stochastic
"microscopic" models. The main emphasis is on models with a nonconserved
order parameter. A slowly varying interface has then a local normal velocity
proportional to the local mean curvature. We study bulk models and effective
interface models and obtain Green-Kubo-like expressions for the mobility. Also
discussed are interface motion in the case of a conserved order parameter, pure
surface diffusion, and interface fluctuations. For the two-dimensional Ising
model at zero temperature, motion by mean curvature is established rigorously