Recent developments in dilute polymer solution rheology are reviewed, and placed within the context of the general goals of predicting the complex flow of complex fluids. In particular, the interplay between the use of polymer kinetic theory and continuum mechanics to advance the microscopic and the macroscopic description, respectively, of dilute polymer solution rheology is delineated. The insight that can be gained into the origins of the high Weissenberg number problem through an analysis of the configurational changes undergone by a single molecule at various locations in the flow domain is discussed in the context of flow around a cylinder confined between flat plates. The significant role played by hydrodynamic interactions as the source of much of the richness of the observed rheological behaviour of dilute polymer solutions is highlighted, and the methods by which this phenomenon can be incorporated into a macroscopic description through the use of closure approximations and multiscale simulations is discussed.