In this talk I will discuss recent efforts in constructing toy models of quantum gravity with the noncommutative framework of finite real spectral triples. Such models can be realized as random matrix integrals, where integration is over some space of finite dimensional Dirac operators. They are appropriately dubbed Dirac ensembles. Even in the simplest settings Dirac ensembles already exhibit interesting behavior. For example, near spectral phase transitions they have been proven to exhibit manifold-like behavior and in many cases one can recover Liouville quantum gravity in an appropriate limit. I will give a general introduction to this relatively new area of study while highlighting recent results. This talk is based on my joint work with H. Hessam, M. Khalkhali, and L. Verhoeven.