It is commonly believed that a fundamental definition of quantum field theory requires the existence of an UV fixed point. Asymptotic freedom of QCD is the well-known example where the fixed point is non-interacting. In this talk, I provide a proof of existence for novel classes of 4D matter-gauge theories whose high-energy behaviour is governed by an interacting UV fixed point. In the absence of asymptotic freedom, scalars, fermions, and non-Abelian gauge fields cooperate in such a way that an interacting UV fixed point emerges. I discuss the key characteristics of these theories which are all under strict perturbative control. I also discuss recent advances and challenges to find interacting UV fixed points in 4D quantum gravity once couplings become large.