  We review recent theoretical and experimental progresses in the coherent
multiple scattering of weakly interacting disordered Bose gases. These systems
have allowed, in the recent years, a characterization of weak and strong
localization phenomena in disorder at an unprecedented level of control. In
this paper, we first discuss the main physical concepts and recent experimental
achievements associated with a few emblematic "mesoscopic" effects in disorder
like coherent back scattering, coherent forward scattering or mesoscopic echos,
focusing on the context of out-of-equilibrium cold-atom setups. We then address
the role of weak particle interactions and explain how, depending on their
relative strength with respect to the disorder and on the time scales probed,
they can give rise to a dephasing mechanism for weak localization, thermalize a
non-equilibrium Bose gas or make it become a superfluid.
