  We describe a random matrix approach that can provide generic and readily
soluble mean-field descriptions of the phase diagram for a variety of systems
ranging from QCD to high-T_c materials. Instead of working from specific
models, phase diagrams are constructed by averaging over the ensemble of
theories that possesses the relevant symmetries of the problem. Although
approximate in nature, this approach has a number of advantages. First, it can
be useful in distinguishing generic features from model-dependent details.
Second, it can help in understanding the `minimal' number of symmetry
constraints required to reproduce specific phase structures. Third, the
robustness of predictions can be checked with respect to variations in the
detailed description of the interactions. Finally, near critical points, random
matrix models bear strong similarities to Ginsburg-Landau theories with the
advantage of additional constraints inherited from the symmetries of the
underlying interaction. These constraints can be helpful in ruling out certain
topologies in the phase diagram. In this Key Issue, we illustrate the basic
structure of random matrix models, discuss their strengths and weaknesses, and
consider the kinds of system to which they can be applied.
