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Causal Dynamical Triangulations (CDT) is a candidate theory for quantum gravity, formulated nonperturbatively as the scaling limit of a lattice theory in terms of triangulated spacetimes. An important feature of this approach is its elegant resolution of the problem of diffeomorphism symmetry in the full, background-free quantum theory. This has enabled the concrete computation of geometric observables in a highly nonperturbative, Planckian regime, an important step in putting quantum gravity on a quantitative footing, and understanding the structure of quantum spacetime. While the need to find quantum observables describing this regime is common to all approaches, CDT provides a concrete testing ground for implementation and measurements. In particular, a new notion of quantum Ricci curvature has opened a new window on the counterintuitive properties of quantum geometry.