In this talk I will give a review of recent progress of the study of random matrix models suggested by noncommutative geometry. We refer to such models as Dirac ensembles which consist of finite real spectral triples where the space of possible Dirac operators is assigned a probability distribution. These Dirac ensembles were originally conceived by J. Barrett and L. Glaser as toy models of Euclidean quantum gravity on finite noncommutative spaces, and have since been found to display various interesting phenomena. For example near spectral phase transitions they exhibit manifold like behavior and in certain cases one can recover Liouville quantum gravity in the double scaling limit. I will highlight general known properties of Dirac ensembles that have been explored as well as some interesting frontiers. This talk is based on my work with H. Hessam and M. Khalkhali.