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Over the years, a number of discrete quantum gravity theories have been proposed in an attempt to find a meaningful regularization scheme for the path-integral formulation of gravity. Nowadays, the so-called Causal Dynamical Triangulation (CDT) model is perhaps the most well-known of them. From the mathematical point of view, in the CDT approach space-time is described by certain random graphs and matter fields are inserted into the model by running statistical mechanical systems on such graphs. In this talk I will review the basic ideas of the CDT model, together with some know results, and I will discuss recent developments in the study of the Ising model coupled with the 2-dimensional causal dynamical triangulation.