We will present the state of the art in PN gravity, and its significant advancement via the EFT of spinning gravitating objects. First, we will introduce the concept of a tower of EFTs for the binary inspiral problem. We will then go over the intricate formulation of the EFT of spinning objects. Finally, we will present some advanced recent results accomplished within this framework. [please email a.held@imperial.ac.uk for zoom link or password]

This talk presents the progress made in my research via the introduction of effective field theories (EFTs) into post-Newtonian (PN) gravity. These have been put forward in the context of gravitational waves (GWs) from the compact binary inspiral. The setup and the strategy of a multi-stage EFT framework, which is deployed for the PN binary inspiral problem, is outlined. I then present in more detail the study of two effective theories at the intermediate scales of the problem. First, the EFT for a single rotating compact object is considered, from which I proceed to the EFT of a compact binary system, viewed as a composite particle with internal binding interactions. I conclude with the prospects of building on the field, and using further modern field theory insights and tools, to address the study of GWs, as well as to expand our fundamental understanding of QFTs and gravity theories at all scales.