Abstract: Three of the four fundamental forces of Nature are successfully described by local quantum field theories. But what is up with gravity? It is well known that the standard quantisation programme for gravity faces problems, and one may wonder whether a quantum field theoretical description is possible at all. In this talk, the scenario of asymptotic safety is explained, according to which gravity achieves a non-trivial fixed point at high energies. Some strong indications for asymptotic safety are reviewed, together with implications for eg. the physics of black holes and high-energetic particle scattering.