  We discuss various aspects of most general multisupport solutions to matrix
models in the presence of hard walls, i.e., in the case where the eigenvalue
support is confined to subdomains of the real axis. The structure of the
solution at the leading order is described by semiclassical, or generalized
Whitham--Krichever hierarchies as in the unrestricted case. Derivatives of
tau-functions for these solutions are associated with families of Riemann
surfaces (with possible double points) and satisfy the
Witten--Dijkgraaf--Verlinde--Verlinde equations. We then develop the
diagrammatic technique for finding free energy of this model in all orders of
the 't~Hooft expansion in the reciprocal matrix size generalizing the Feynman
diagrammatic technique for the Hermitian one-matrix model due to Eynard.
