  We review the description of scalar field theories on fuzzy spaces by
Hermitian random matrix models. After reminding the reader of the relevant
aspects of the random matrix theory and construction of the fuzzy spaces, we
summarize the most important results for the scalar fields on such spaces. We
then introduce the multi-trace matrix models relevant for the analytical
description of scalar field theories on fuzzy spaces and show to what extent
they do, and to what extent they do not, describe the know phase structure of
$\phi^4$ theory on the fuzzy sphere.
