In recent years, new theories of particle physics have been discovered whose short-distance behaviour is controlled by an interacting (rather than a free) UV fixed point. The very existence of these asymptotically safe particle theories has opened up new directions to UV-complete the Standard Model of particle physics beyond the paradigm of asymptotic freedom. In this talk, I give a systematic overview of QCD-like theories with weakly and strongly coupled fixed points, with and w/o supersymmetry, and discuss key features. Concrete applications for BSM physics are also given. If time permits, I briefly outline how some of these ideas and insights are used to understand the quantisation of gravity.