  A powerful strategy to treat quantum field theories beyond perturbation
theory is by putting them on a lattice. However, the dynamical and symmetry
structure of general relativity have for a long time stood in the way of a
well-defined lattice formulation of quantum gravity. These issues are resolved
by using Causal Dynamical Triangulations (CDT) to implement a nonperturbative,
background-independent path integral for Lorentzian quantum gravity on
dynamical lattices. We describe the essential ingredients of this formulation,
and how it has allowed us to move away from formal considerations in quantum
gravity to extracting quantitative results on the spectra of
diffeomorphism-invariant quantum observables, describing physics near the
Planck scale. Key results to date are the emergence of a de Sitter-like quantum
universe and the discovery of an anomalous spectral dimension at short
distances.
