  This article is an overview of the use of so-called Euclidean Dynamical
Triangulations (EDT) and Causal Dynamical Triangulations (CDT) as lattice
regularizations of quantum gravity. The lattice regularizations have been very
successful in the case of two-dimensional quantum gravity, where the lattice
theories indeed provide regularizations of continuum well defined quantum
gravity theories. In four-dimensional spacetime the Einstein-Hilbert action
leads to a theory of gravity which is not renormalizable as a perturbative
quantum theory around flat spacetime. It is discussed how lattice gravity in
the form of EDT or CDT can be used to search for a non-perturbative UV fixed
point of the lattice renormalization group in the spirit of asymptotic safety.
In this way it might be possible to define a quantum theory of gravity also at
lengthscales smaller than the Planck length.
