Ultraviolet fixed points provide an important means to define continuum limits of quantum field
theories. In this contribution, we explain how interacting ultraviolet fixed points may arise in
general four-dimensional gauge theories coupled weakly to scalar and fermionic matter fields.
Our results derive from a systematic classification of all high- and low-energy fixed points in
general gauge theories within perturbation theory. It is shown why and how Yukawa interactions
provide a unique mechanism for the generation of perturbative ultraviolet fixed points. Phase
diagrams for simple gauge theories are discussed to illustrate the main results. Some implications
for particle physics beyond the Standard Model are indicated.