  We review the integrable structure of the Dirichlet boundary problem in two
dimensions. The solution to the Dirichlet boundary problem for simply-connected
case is given through a quasiclassical tau-function, which satisfies the Hirota
equations of the dispersionless Toda hierarchy, following from properties of
the Dirichlet Green function. We also outline a possible generalization to the
case of multiply-connected domains related to the multi-support solutions of
matrix models.
