  We compute exact solutions of two--matrix models, i.e. detailed genus by
genus expressions for the correlation functions of these theories, calculated
without any approximation. We distinguish between two types of models, the
unconstrained and the constrained ones. Unconstrained two--matrix models
represent perturbations of $c=1$ string theory, while the constrained ones
correspond to topological field theories coupled to topological gravity. Among
the latter we treat in particular detail the ones based on the KdV and on the
Boussinesq hierarchies.
