  In this Chapter, we present recent theoretical developments on the finite
temperature transport of one dimensional electronic and magnetic quantum
systems as described by a variety of prototype models. In particular, we
discuss the unconventional transport and dynamic - spin, electrical, thermal -
properties implied by the integrability of models as the spin-1/2 Heisenberg
chain or Hubbard. Furthermore, we address the implication of these developments
to experimental studies and theoretical descriptions by low energy effective
theories.
