Asymptotic freedom is a key ingredient in the successful construction of
the Standard Model of particle physics. It has been conjectured long ago
that gravity may equally well fit into this picture - despite its
notorious perturbative non-renormalisability - provided that the theory
turns out to be asymptotically safe. We contrast asymptotic freedom with
asymptotic safety and propose a self-consistent search strategy for the
latter. Results for a simplified version of quantum gravity and
implications for the asymptotic safety conjecture are discussed.