  The general features of the 1/N expansion in statistical mechanics and
quantum field theory are briefly reviewed both from the theoretical and from
the phenomenological point of view as an introduction to a more detailed
analysis of the large-N properties of spin and gauge models possessing the
symmetry group $SU(N) \times SU(N)$.
  An extensive discussion of the known properties of the single-link integral
(equivalent to YM_2 and one-dimensional chiral models) includes finite-$N$
results, the external field solution, properties of the determinant, and the
double scaling limit.
  Two major classes of solvable generalizations are introduced: one-dimensional
closed chiral chains and models defined on a $d-1$ dimensional simplex. In both
cases large-N solutions are presented with emphasis on their double scaling
properties.
  The available techniques and results concerning unitary-matrix models that
correspond to asymptotically free quantum field theories (two-dimensional
chiral models and four-dimensional QCD) are discussed, including
strong-coupling methods, reduced formulations, and the Monte Carlo approach.
