Field theory for gravity at all scales

Abstract: We review here the main advances made by using effective field theories (EFTs) in classical gravity, with notable focus on those unique to the EFTs of post-Newtonian (PN) gravity. We then proceed to overview the various prospects of using field theory to study the real-world gravitational wave (GW) data, as well as to ameliorate our fundamental understanding of gravity at all scales, by going from the EFTs of PN gravity to modern advances in scattering amplitudes, including computational techniques and intriguing duality relations between gauge and gravity theories.