  We review the interplay of fuzzy field theories and matrix models, with an
emphasis on the phase structure of fuzzy scalar field theories. We give a
self-contained introduction to these topics and give the details concerning the
saddle point approach for the usual single trace and multitrace matrix models.
We then review the attempts to explain the phase structure of the fuzzy field
theory using a corresponding random matrix ensemble, showing the strength and
weaknesses of this approach. We conclude with a list of challenges one needs to
overcome and the most interesting open problems one can try to solve.
