Many of the practical applications of macromolecules, such as the increase of the viscosity of an oil by polymeric additives or the shear-thinning effect in a paint are related to their very unusual hydrodynamic and rheological behaviour. Polymeric liquids (i.e. macromolecular solutions, or molten polymers in a liquid state without any solvent) do not behave as classical Newtonian liquids which can be characterized by a viscosity independent of the applied velocity gradient, they are non-Newtonian viscoelastic fluids: after the application of an external deformation (such as stretching a chewing-gum) a polymeric liquid first behaves as an elastic solid or a rubber, the stress does not vanish and is proportional to the deformation; after a finite relaxation time, the stress relaxes to zero thus showing a liquid behaviour. Moreover, macromolecules, being large objects (the individual size might be as large as 1 μm), their motions are very slow and the relaxation times involved can be as large as seconds. This, in turn, leads to viscosities which can be as high as 105poise for polymer melts in the limit of vanishing shear rates.