  In this talk I discuss both the present status and some recent work on the
Kazakov--Migdal Model which was originally proposed as a soluble, large $N$
realization of QCD. After a brief description of the model and a discussion of
its solubility in the large $N$ limit I discuss several of the serious problems
with the model which lead to the conclusion that it does {\it not} induce QCD.
The model is nonetheless a very interesting example of a Gauge Theory and it is
related to some very interesting Matrix Models. I then outline a technique
\REF\dmsxyz{\dms}\refend which uses ``Loop Equations'' for solving such models.
A Penner--like model is then discussed with two logarithmic singularities. This
model is distinguished by the fact that it is exactly and explicitly soluble in
spite of the fact that it is not Gaussian. It is shown how to analyze this
model using both a technical approach and from a more physical point of view.
