  The thermally activated creep motion of an elastic interface weakly driven on
a disordered landscape is one of the best examples of glassy universal
dynamics. Its understanding has evolved over the last 30 years thanks to a
fruitful interplay between elegant scaling arguments, sophisticated analytical
calculations, efficient optimization algorithms and creative experiments. In
this article, starting from the pioneer arguments, we review the main
theoretical and experimental results that lead to the current physical picture
of the creep regime. In particular, we discuss recent works unveiling the
collective nature of such ultra-slow motion in terms of elementary activated
events. We show that these events control the mean velocity of the interface
and cluster into "creep avalanches" statistically similar to the deterministic
avalanches observed at the depinning critical threshold. The associated
spatio-temporal patterns of activated events have been recently observed in
experiments with magnetic domain walls. The emergent physical picture is
expected to be relevant for a large family of disordered systems presenting
thermally activated dynamics.
