  We describe the motivation behind the recent formulation of a nonperturbative
path integral for Lorentzian quantum gravity defined through Causal Dynamical
Triangulations (CDT). In the case of two dimensions the model is analytically
solvable, leading to a genuine continuum theory of quantum gravity whose ground
state describes a two-dimensional "universe" completely governed by quantum
fluctuations. One observes that two-dimensional Lorentzian and Euclidean
quantum gravity are distinct. In the second part of the review we address the
question of how to incorporate a sum over space-time topologies in the
gravitational path integral. It is shown that, provided suitable causality
restrictions are imposed on the path integral histories, there exists a
well-defined nonperturbative gravitational path integral including an explicit
sum over topologies in the setting of CDT. A complete analytical solution of
the quantum continuum dynamics is obtained uniquely by means of a double
scaling limit. We show that in the continuum limit there is a finite density of
infinitesimal wormholes. Remarkably, the presence of wormholes leads to a
decrease in the effective cosmological constant, reminiscent of the suppression
mechanism considered by Coleman and others in the context of a Euclidean path
integral formulation of four-dimensional quantum gravity in the continuum. In
the last part of the review universality and certain generalizations of the
original model are discussed, providing additional evidence that CDT define a
genuine continuum theory of two-dimensional Lorentzian quantum gravity.
