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

Ultraviolet Divergences and Scale-Dependent Gravitational Couplings