I consider nonequilibrium time evolution in the presence of inhomogeneities in integrable systems. I remind the audience of the so-called generalized hydrodynamic (GHD) description, and I present some recent results obtained in the massive XXZ spin-1/2 chain.
In particular, I show examples of dynamics with a sub-ballistic (perhaps diffusive) behavior. The ambition to describe such regimes is a strong motivation to go beyond GHD. Using noninteracting spin chains as a workbench, I point out some of the problems that have to be overcome in order to improve on the current theory.