Abstract: In the era of gravitational wave astronomy it is necessary to contrast the detected waveforms produced in mergers of compact objects with the predictions from general relativity and also from alternative theories of gravity. However, to be able to do so, such alternative theories of gravity ought to have a well-posed initial value problem. In this talk I will explain how one can formulate the initial value problem for a wide class of alternative theories of gravity that have attracted the attention of the community by thinking about them as classical effective field theories. Furthermore, I will show how one can consistently compute, from first principles, the waveforms produced in binary black hole  mergers in these theories. These results open the way to test these theories in present and future gravitational wave observations.