During flow, an initially homogeneous polymer solution may develop position-dependent concentration gradients due to migration of the polymer molecules with respect to the bulk flow. We review the experimental evidence, especially the anomalous experimental observations of interest to engineers, concerned with enhancement (which is sometimes rather dramatic) in heat, mass and momentum transfer during the flow of such "slipping fluids". Further, we critically review and discuss the merits of various heuristic and more fundamental fluid mechanical or thermodynamic models, which attempt to explain this phenomenon. We show that many theoretical predictions are often in conflict with each other even qualitatively, and the reported studies providing direct experimental evidence are few. Directions for future work in the area have been highlighted.