The quantum spacetime of c>0 2d gravity

We review recent developments in the understanding of the fractal properties of quantum spacetime of 2d gravity coupled to c > 0 conformal matter. In particular we discuss bounds put by numerical simulations using dynamical triangulations on the value of the Hausdorff dimension d(H) obtained from scaling properties of two point functions defined in terms of geodesic distance. Further insight to the fractal structure of spacetime is obtained from the study of the loop length distribution function which reveals that the 0 < c less than or equal to 1 system has similar geometric properties with pure gravity, whereas the branched polymer structure becomes clear for c greater than or equal to 5.