Gravitational waves emitted by black hole binaries enable unprecedented tests of the theory of gravity at highly non-linear regimes. The current gravitational wave-based tests of gravity are parametrized or null tests against General Relativity which remain limited when interpreting theoretical constraints. Going beyond the current tests requires accurate theoretical modelling of the waveforms in viable extensions of General Relativity. In this talk I will present the recent results and physical insights from analytical modelling of the gravitational waves in the so-called Einstein scalar Gauss Bonnet gravity. Being a sub-class of both Horndeski and quadratic gravities, this theory introduces non-linear curvature corrections to strong-field regime of gravity, allows for hairy-black hole solutions, and scalar-induced tidal deformations. I will explain the modelling and gravitational-wave signatures of theory’s curvature corrections, as well as scalar tidal deformations, to first post-Newtonian order and will further discuss the prospects of testing the features of this theory through gravitational wave observations.