  We review some of the recent results on equilibration of one-dimensional
quantum liquids. The low-energy properties of these systems are described by
the Luttinger liquid theory, in which the excitations are bosonic
quasiparticles. At low temperatures the relaxation of the gas of excitations
toward full equilibrium is exponentially slow. In electronic Luttinger liquids
these relaxation processes involve backscattering of electrons and give rise to
interesting corrections to the transport properties of one-dimensional
conductors. We focus on the phenomenological theory of the equilibration of a
quantum liquid and obtain an expression for the relaxation rate in terms of the
excitation spectrum.
