Quantum Gravity by Causal Dynamical Triangulation has over the last few years
emerged as a serious contender for a nonperturbative description of the theory.
It is a nonperturbative implementation of the sum-over-histories, which relies
on few ingredients and initial assumptions, has few free parameters and -
crucially - is amenable to numerical simulations. It is the only approach to
have demonstrated that a classical universe can be generated dynamically from
Planckian quantum fluctuations. At the same time, it allows for the explicit
evaluation of expectation values of invariants characterizing the highly
nonclassical, short-distance behaviour of spacetime. As an added bonus, we have
learned important lessons on which aspects of spacetime need to be fixed a
priori as part of the background structure and which can be expected to emerge
dynamically.Comment: To appear in "Foundations of Space and Time", Cambridge Univ. Press,
eds. G. Ellis, J. Murugan, A Weltma