  While Fourier's law is empirically confirmed for many substances and over an
extremely wide range of thermodynamic parameters, a convincing microscopic
derivation still poses difficulties. With current machines the solution of
Newton's equations of motion can be obtained with high precision and for a
reasonably large number of particles. For simplified model systems one thereby
arrives at a deeper understanding of the microscopic basis for Fourier's law.
We report on recent, and not so recent, advances.
