Two- dimensional fluid flows exhibit a variety of coherent structures such as vortices and dipoles which can often serve as organizing centers for the flow. These coherent structures can sometimes be associated with the existence of special geometrical structures in the phase space of the equations and in these cases the evolution of these flows can often be studied with the aid of dynamical systems theory. The dynamical systems ideas also suggest new ways of numerically studying such coherent structures and I will describe recent results which generalize the classical point vortex model to systematically include the effects of viscosity and finite core size.