The Whitham equations are a corestone of the perturbation theory of thesoliton equations. They are deeply connected with structures oftopological quantum field theories (WDVV equations), and with the Seiberg-Wittensolution of N=2 supersymmetric gauge models. Recently, it wasdiscovered that special solutions of the Whitham equations describeconformal maps. In the talk this surprising connection will be discussedand the concept of tau-function of conformal maps will be introduced.