  We review recent progress in 2D gravity coupled to $d<1$ conformal matter,
based on a representation of discrete gravity in terms of random matrices. We
discuss the saddle point approximation for these models, including a class of
related $O(n)$ matrix models. For $d<1$ matter, the matrix problem can be
completely solved in many cases by the introduction of suitable orthogonal
polynomials. Alternatively, in the continuum limit the orthogonal polynomial
method can be shown to be equivalent to the construction of representations of
the canonical commutation relations in terms of differential operators. In the
case of pure gravity or discrete Ising--like matter, the sum over topologies is
reduced to the solution of non-linear differential equations (the Painlev\'e
equation in the pure gravity case) which can be shown to follow from an action
principle. In the case of pure gravity and more generally all unitary models,
the perturbation theory is not Borel summable and therefore alone does not
define a unique solution. In the non-Borel summable case, the matrix model does
not define the sum over topologies beyond perturbation theory. We also review
the computation of correlation functions directly in the continuum formulation
of matter coupled to 2D gravity, and compare with the matrix model results.
Finally, we review the relation between matrix models and topological gravity,
and as well the relation to intersection theory of the moduli space of
punctured Riemann surfaces.
