  We argue that theories of quantum gravity constructed with the help of
(Causal) Dynamical Triangulations have given us the most informative,
quantitative models to date of quantum spacetime. Most importantly, these are
derived dynamically from nonperturbative and background-independent quantum
theories of geometry. In the physically relevant case of four spacetime
dimensions, the ansatz of Causal Dynamical Triangulations produces - from a
fairly minimal set of quantum field-theoretic inputs - an emergent spacetime
which macroscopically looks like a de Sitter universe, and on Planckian scales
possesses unexpected quantum properties. Important in deriving these results
are a regularized version of the theory, in which the quantum dynamics is well
defined, can be studied with the help of numerical Monte Carlo methods and
extrapolated to infinite lattice volumes.
