The purpose of this article is to review molecular dynamics simulation of transport processes of liquid crystal model systems carried out during the last 30 years. In those processes a thermodynamic force or an external dissipative field drives a thermodynamic flux. Well-known examples are shear-flow and elongational flow, where a velocity gradient gives rise to a shear stress, and heat conduction where a temperature gradient drives a heat flow. In these transport processes it has been found that the director of the liquid crystal orients at a constant angle relative to the external dissipative field: In shear-flow the director orients at a constant angle relative to the streamlines, in elongational flow the director is either parallel or perpendicular to the elongation direction and during heat conduction the director is either parallel or perpendicular to the temperature gradient. The alignment angle has been found to be the one that minimizes the irreversible energy dissipation rate. This is in accordance with a recently proven theorem stating that this quantity is minimal in the linear regime of a non-equilibrium steady state. The most commonly used model system is based on the Gay-Berne fluid which can be regarded as a Lennard-Jones fluid generalized to elliptical molecular cores.