  In this paper, we will critically discuss recent theoretical and experimental
developments on the transport of one dimensional quantum systems. In
particular, we will focus on open issues and controversial results related to
the finite temperature dynamics of integrable quantum models. These singular
systems are commonly used in the description of quasi-one dimensional
materials. They have recently attracted a lot of interest in connection to the
interpretation of experiments, specially after the discovery of unusual thermal
conductivity in magnetic compounds.
