We consider the hydrodynamics of creatures capable of sustaining themselves on the water surface by means other than flotation. Particular attention is given to classifying water walkers according to their principal means of weight support and lateral propulsion. The various propulsion mechanisms are rationalized through consideration of energetics, hydrodynamic forces applied, or momentum transferred by the driving stroke. We review previous research in this area and suggest directions for future work. Special attention is given to introductory discussions of problems not previously treated in the fluid mechanics literature, with hopes of attracting physicists, applied mathematicians, and engineers to this relatively unexplored area of fluid mechanics.