Abstract: In this talk I will give an overview of the various approaches in modelling self-consistently higher derivative theories of gravity. In the first part, I will discuss the modifications of the standard gauges used in numerical relativity, focusing on the most general scalar tensor theory of gravity up to four derivatives and Lovelock’s gravity as examples. In the second part, I will discuss higher derivative theories of gravity with higher order equations of motion and how to extract their physical observables. In particular, I will discuss recent developments that show that all polynomial higher derivative theories of gravity have a well-posed initial value formulation.