  I review the field-theoretic renomalization group approach to quantum
gravity, built around the existence of a non-trivial ultraviolet fixed point in
four dimensions. I discuss the implications of such a fixed point, found in
three largely unrelated non-perturbative approaches, and how it relates to the
vacuum state of quantum gravity, and specifically to the running of $G$. One
distinctive feature of the new fixed point is the emergence of a second
genuinely non-perturbative scale, analogous to the scaling violation parameter
in non-abelian gauge theories. I argue that it is natural to identify such a
scale with the small observed cosmological constant, which in quantum gravity
can arise as a non-perturbative vacuum condensate.
  (Plenary Talk, 12-th Marcel Grossmann Conference on Recent Developments in
General Relativity, Astrophysics and Relativistic Field Theories, UNESCO Paris,
July 12-18, 2009).
