The strong-field spacetime near a compact-object binary is rich with information about gravitational interactions, yet capturing it faithfully remains a formidable challenge for theoretical models. This conference addresses that challenge by focusing on the critical interfaces between four approaches: matching weak-field analytical results to the strong-field regime, modelling nonlinearities across the inspiral, merger, and ringdown phases, and connecting theoretical waveform predictions to observational data analysis. It will bring together experts in black hole perturbation theory, ringdown physics, scattering amplitudes, effective field theory, numerical relativity, and data analysis for intensive exchange, with the aim of building the collaborations needed to extract the physics encoded in the next generation of gravitational-wave observations.