  In this thesis we investigate the importance of causality in non-perturbative
approaches to quantum gravity. Firstly, causal sets are introduced as a simple
kinematical model for causal geometry. It is shown how causal sets could
account for the microscopic origin of the Bekenstein entropy bound. Holography
and finite entropy emerge naturally from the interplay between causality and
discreteness. Going beyond causal set kinematics is problematic however. It is
a hard problem to find the right amplitude to attach to each causal set that
one needs to define the non-perturbative quantum dynamics of gravity. One
approach which is ideally suited to define the non-perturbative gravitational
path integral is dynamical triangulation. Without causality this method leads
to unappealing features of the quantum geometry though. It is shown how
causality is instrumental in regulating this pathological behavior. In two
dimensions this approach of causal dynamical triangulations has been
analytically solved by transfer matrix methods. In this thesis considerable
progress has been made in the development of more powerful techniques for this
approach. The formulation through matrix models and a string field theory allow
us to study interesting generalizations. Particularly, it has become possible
to define the topological expansion. A surprising twist of the new matrix model
is that it partially disentangles the large-N and continuum limit. This makes
our causal model much closer in spirit to the original idea by 't Hooft than
the conventional matrix models of non-critical string theory.
