The uses of Whitham hierarchies

We review some of the uses of Whitham hierarchies in the context of the theory of the prepotential in N = 2 supersymmetric gauge theories. We focus on the structure of the contact terms in the twisted topological theory, and on the connection between Whitham hierarchies and the u-plane integrals for higher rank gauge groups, trying to put together the different approaches involved in this connection. We also review two other uses of the Whitham hierarchies: the interpretation of the slow times as supersymmetry breaking parameters, and the new techniques to extract instanton corrections using the RG equations written in terms of theta functions.