Transport out of equilibrium in the presence of strong interactions remains one of the most active and difficult topics in condensed matter physics, be it theoretical, numerical, or experimental. Finding a non trivial, solvable example where things could be computed exactly using the Bethe ansatz would be a major conceptual step. I will review attempts in this direction of the past 15 years, together with what seems to be a first, unambiguously positive result.

IPhT