With the advent of gravitational wave astronomy in 2015, understanding the evolution of compact binary systems (black holes and/or neutron stars in gravitationally bound orbits) has become a subject of direct experimental relevance. In this talk, I will discuss how effective field theory ideas that originated in high energy physics and condensed matter can be brought to bear on the theoretical description of gravitational radiation from black hole or neutron star mergers. I begin the talk with a brief overview of the LIGO/VIRGO gravitational wave interferometer, and explain the necessity of constructing high precision theoretical waveform templates in order to fully extract physics from LIGO observations. I will then describe an effective field theory of interacting gravitons which can be used to efficiently extract the predictions of classical general relativity for the evolution of compact binaries in the initial “adiabatic” phase of the merger. The last part of the talk will focus on the role that finite size effects due to the event horizon play in the dynamics of classical and quantum black holes, with applications both to the phenomenology of black hole mergers at LIGO, as well as more formally to the black hole S-matrix in quantum gravity.