Explore binary black hole mergers in cubic Horndeski theory through this 42-minute conference talk presented by Pau Figueras of Queen Mary, University of London at IPAM's Workshop II: Mathematical and Numerical Aspects of Gravitation. Delve into the well-posed initial value problem in the standard CCZ4 formulation of Einstein equations and examine how Horndeski terms, treated fully non-linearly, impact binary mergers while remaining within the effective field theory regime. Discover how small effects accumulate over time, leading to significant differences compared to general relativity. Gain insights into studying black hole binaries in higher derivative theories of gravity, covering topics such as weakly coupled regimes, linearization, binary studies, waveforms, and potential implications for gravitational wave astronomy.