It is commonly believed that for a quantum field theory to be fundamental, its high-energy behaviour must be governed by an ultraviolet (UV) fixed point. A very satisfying example is given by asymptotic freedom of QCD where the UV fixed point is non-interacting. In this talk, I discuss the existence of interacting UV fixed points in various quantum field theories, in particular in four dimensions, both with and without gravity. Implications for particle physics are also evaluated.