  Recent results on theoretical studies of heat conduction in low-dimensional
systems are presented. These studies are on simple, yet nontrivial, models.
Most of these are classical systems, but some quantum-mechanical work is also
reported. Much of the work has been on lattice models corresponding to phononic
systems, and some on hard particle and hard disc systems. A recently developed
approach, using generalized Langevin equations and phonon Green's functions, is
explained and several applications to harmonic systems are given. For
interacting systems, various analytic approaches based on the Green-Kubo
formula are described, and their predictions are compared with the latest
results from simulation. These results indicate that for momentum-conserving
systems, transport is anomalous in one and two dimensions, and the thermal
conductivity kappa, diverges with system size L, as kappa ~ L^alpha. For one
dimensional interacting systems there is strong numerical evidence for a
universal exponent alpha =1/3, but there is no exact proof for this so far. A
brief discussion of some of the experiments on heat conduction in nanowires and
nanotubes is also given.
