In this talk I will show how to derive analytical gravitational waveforms associated to the coalescence of a “hairy” black hole binary in Einstein-scalar-Gauss-Bonnet gravity (ESGB). I will present the post-Newtonian (PN) Lagrangian and gravitational wave fluxes associated to such systems. The PN framework relies on reducing the black holes to point particles with scalar field-dependent masses. In light of the first law of thermodynamics of ESGB black holes, I will show that this procedure amounts to fixing the Wald entropy of each black hole during their slow, adiabatic inspiral. I will then extend the scope of the PN approximation to the strong field regime near merger by generalizing the Effective-One-Body (EOB) formalism to ESGB gravity.