  The understanding of the underlying dynamical mechanisms which determine the
macroscopic laws of heat conduction is a long standing task of non-equilibrium
statistical mechanics. A better understanding of the mechanism of heat
conduction may lead to potentially interesting applications based on the
possibility to control the heat flow. Indeed, different models of thermal
rectifiers has been recently proposed in which heat can flow preferentially in
one direction. Although these models are far away from a prototype realization,
the underlying mechanisms are of very general nature and, as such, are suitable
of improvement and may eventually lead to real applications. We briefly discuss
the problem of heat transport in classical and quantum systems and its relation
to the chaoticity of the dynamics. We then study the phenomenon of thermal
rectification and briefly discuss the different types of microscopic mechanisms
that lead to the rectification of heat flow.
