The method of non-equilibrium molecular dynamics, with special emphasi
s on the simulation of a plane Couette flow, and results for simple fl
uids are reviewed briefly. Then simulation data are presented for comp
lex fluids, in particular for polymeric liquids and anisotropic fluids
such as nematic liquid crystals (LC) and ferro-fluids, magneto- or el
ectro-rheological (MR or ER) fluids.