  A review of the relationships between matrix models and noncommutative gauge
theory is presented. A lattice version of noncommutative Yang-Mills theory is
constructed and used to examine some generic properties of noncommutative
quantum field theory, such as UV/IR mixing and the appearence of
gauge-invariant open Wilson line operators. Morita equivalence in this class of
models is derived and used to establish the generic relation between
noncommutative gauge theory and twisted reduced models. Finite dimensional
representations of the quotient conditions for toroidal compactification of
matrix models are thereby exhibited. The coupling of noncommutative gauge
fields to fundamental matter fields is considered and a large mass expansion is
used to study properties of gauge-invariant observables. Morita equivalence
with fundamental matter is also presented and used to prove the equivalence
between the planar loop renormalizations in commutative and noncommutative
quantum chromodynamics.
