We discuss the low-temperature dynamics of an elastic manifold driven
through a random medium. For driving forces well below the T = 0 depin
ning force, the medium advances via thermally activated hops over the
energy barriers separating favorable metastable states. We show that t
he distribution of waiting times for these hopping processes scales as
a power law. This power-law distribution naturally yields a nonlinear
glassy response for the driven medium, v similar to exp(-const x F--m
u).