I will discuss how cutting-edge amplitudes methods can be applied to the study of classical binary dynamics in general relativity relevant to gravitational wave physics. After a more general overview I will introduce the heavy mass effective field theory (HEFT) as an efficient implementation of these ideas to compute the classical deflection angle and waveforms in GR. I will also describe a novel version of the color-kinematics duality for amplitudes in HEFT and Yang-Mills and discuss its underlying kinematic Hopf algebra.