  This article discusses the infrared and the (perspective) ultraviolet limits
of four-dimensional Causal Dynamical Triangulations (CDT). CDT is a
non-perturabtive and background-independent approach to quantization of
Einstein's gravity, based on a lattice regularization of the
quantum-gravitational path integral. It is shown that inside the, so-called, de
Sitter phase one recovers a four-dimensional semiclassical universe, where
behaviour of the scale factor is consistent with classical solutions of
Einstein's field equations and fluctuations of the scale factor are very
accurately described by a simple minisuperspace effective action. It is argued
that some of the phase transitions bordering the semiclassical phase are
higher-order transitions, which opens a possibility of defining a continuum
limit of CDT. Finally, it is discussed how to define the renormalization group
flow in CDT and then how to search for a UV fixed point in which, in the spirit
of asymptotic safety, quantum theory of gravity could become non-perturbatively
renormalizable and thus valid up to arbitrarily short distance scales.
