Viscoelastic fluids, in particular polymer solutions and melts, show a multitude of phenomena which appear quite bizarre when compared to the familiar behaviour of Newtonian fluids. For example, they exhibit die swell when flowing out of capillaries and dies, they climb up the shafts of rotating stirrers, secondary flows occur in straight pipes with non-circular cross-section, the direction of secondary flows around rotating bodies can be opposite to that in Newtonian fluids, and they can be lifted up many centimetres in a free jet.For a phenomenological description of such flow behaviour, the governing constitutive equations are generally of the functional type relating the histories of stress and strain in a non-linear way. Somewhat analogous to the theorems of classical thermodynamics, there exist some general principles by which the set of functionals is restricted to those signifying "admissible constitutive equations", although for more detailed predictions statistical models are required. These models are also somewhat analogous to those of statistical thermodynamics and the kinetic theory of gases and liquids.Such statistical models are at present best developed for polymer fluids. It is shown that by generalizing the simple model of a dilute solution of Hookean dumbbell molecules it is possible to construct molecular models that enable the above-mentioned and related phenomena to be predicted at least qualitatively for dilute as well as concentrated polymer systems.