This subject combines ideas from quantum field theory on noncommutative spaces with technologies developed for matrix models to rigorously compute all renormalised correlation functions of these toy models. There is a natural projection of matricial correlation functions to Schwinger functions of an ordinary Euclidean quantum field theory. The main question we are working on is whether or not these functions satisfy Osterwalder-Schrader reflection positivity. If so the model would define a true relativistic (but very simple) quantum field theory in four dimensions. We have partial results that this could be the case.