The last 10 years gravitational wave observations have allowed us to finally probe the strong field, nonlinear dynamics of gravity and have produced interesting bounds on deviations from General Relativity and the existence of new light fields. In the same period our theoretical understanding of how such deviation can arise and get imprinted on waveform have also progressed significantly. I will draw some lesson from this theoretical progress and discuss how it can inform the way we search of new physics with gravitational waves.