Asymptotically Safe Gravity and Higher Order Curvatures

In this talk, I will give an introduction to the asymptotic safety conjecture of quantum gravity and the search for viable non-trivial fixed points. Basic concepts such as fixed points and their UV critical surfaces are discussed and I give a brief overview about results obtained in the literature. Subsequently, I will discuss recent developments regarding the effects of higher order curvature invariants in asymptotic safety and explain their implications.