Glassy dynamics and coarsening

In this paper I present a short review of the present theoretical understanding of the dynamics, global and fluctuating, in the glassy out of equilibrium regime. The first part of the talks dealt with a summary of the results of mean-field models and served to introduce the conjecture that time-reparametrization invariance controls the fluctuating dynamics. Finally, I briefly discussed very recent results on the domain size fluctuations in coarsening problems and how these and similar studies of the dynamics of elastic lines could help us in understanding the evolution of more complex glassy systems.