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We show how it is possible to formulate Euclidean two-dimensional quantumgravity as the scaling limit of an ordinary statistical system by means ofdynamical triangulations, which can be viewed as a discretization in the spaceof equivalence classes of metrics. Scaling relations exist and the criticalexponents have simple geometric interpretations. Hartle-Hawkings wavefunctionals as well as reparametrization invariant correlation functions whichdepend on the geodesic distance can be calculated. The discretized approachmakes sense even in higher dimensional space-time. Although analytic solutionsare still missing in the higher dimensional case, numerical studies reveal aninteresting structure and allow the identification of a fixed point where wecan hope to define a genuine non-perturbative theory of four-dimensionalquantum gravity.Comment: Review, 44 pages, tar compressed uuencoded ps-file (after removing  header, type csh filename.uu

Dynamical triangulations, a gateway to quantum gravity?