  Building a consistent Quantum Theory of Gravity is one of the most
challenging aspects of modern theoretical physics. In the past couple of years,
new attempts have been made along the path of ``asymptotic safety'' through the
use of Exact Renormalisation Group Equations, which hinge on the existence of a
non-trivial fixed point of the flow equations. We will first summarize the
major results that have been obtained along these lines, then we will consider
the effect of introducing matter fields into the theory. Our analyses show that
in order to preserve the existence of the fixed point one must satisfy some
constraints on the matter content of the theory.
