  I review the lattice approach to quantum gravity, and how it relates to the
non-trivial ultraviolet fixed point scenario of the continuum theory. After a
brief introduction covering the general problem of ultraviolet divergences in
gravity and other non-renormalizable theories, I cover the general methods and
goals of the lattice approach. An underlying theme is the attempt at
establishing connections between the continuum renormalization group results,
which are mainly based on diagrammatic perturbation theory, and the recent
lattice results, which apply to the strong gravity regime and are inherently
non-perturbative. A second theme in this review is the ever-present natural
correspondence between infrared methods of strongly coupled non-abelian gauge
theories on the one hand, and the low energy approach to quantum gravity based
on the renormalization group and universality of critical behavior on the
other. Towards the end of the review I discuss possible observational
consequences of path integral quantum gravity, as derived from the non-trivial
ultraviolet fixed point scenario. I argue that the theoretical framework
naturally leads to considering a weakly scale-dependent Newton's costant, with
a scaling violation parameter related to the observed scaled cosmological
constant (and not, as naively expected, to the Planck length).
