In this seminar I will introduce the concept of asymptotic safety. After a general overview, I will focus on weakly coupled, perturbative quantum field theories. Powerful theorems will be introduced, dictating that asymptotic safety requires gauge theories with Yukawa interactions. In the search of concrete realisations, an important toy model will be discussed, where asymptotic safety is perturbatively exact. With this key element at hand, I will report on efforts to construct UV complete extensions of the Standard Model of particle physics.