  The paper contains some new results and a review of recent achievements,
concerning the multisupport solutions to matrix models. In the leading order of
the 't Hooft expansion for matrix integral, these solutions are described by
quasiclassical or generalized Whitham hierarchies and are directly related to
the superpotentials of four-dimensional N=1 SUSY gauge theories. We study the
derivatives of tau-functions for these solutions, associated with the families
of Riemann surfaces (with possible double points), and relations for these
derivatives imposed by complex geometry, including the WDVV equations. We also
find the free energy in subleading order of the 't Hooft expansion and prove
that it satisfies certain determinant relations.
