The paper explores the resonant behavior of ultralight boson clouds around rotating black holes in binary systems, focusing on the gravitational wave (GW) signals these resonances produce. The authors study the nonlinear dynamics of the system, including orbital backreaction and generic eccentricity and inclination, to understand how resonances affect the cloud's evolution and the binary's parameters. They find that resonances can "start" or "break" above critical thresholds, leading to significant changes in the binary's eccentricity and inclination. The study reveals two possible outcomes: if the binary and cloud are close to counter-rotating, the cloud survives until the system enters the GW detection band; otherwise, the cloud is destroyed during a resonance at large separations but leaves an imprint on the binary's parameters. The paper also discusses the observational signatures of these resonances, particularly for future GW detectors like LISA or the Einstein Telescope.The paper explores the resonant behavior of ultralight boson clouds around rotating black holes in binary systems, focusing on the gravitational wave (GW) signals these resonances produce. The authors study the nonlinear dynamics of the system, including orbital backreaction and generic eccentricity and inclination, to understand how resonances affect the cloud's evolution and the binary's parameters. They find that resonances can "start" or "break" above critical thresholds, leading to significant changes in the binary's eccentricity and inclination. The study reveals two possible outcomes: if the binary and cloud are close to counter-rotating, the cloud survives until the system enters the GW detection band; otherwise, the cloud is destroyed during a resonance at large separations but leaves an imprint on the binary's parameters. The paper also discusses the observational signatures of these resonances, particularly for future GW detectors like LISA or the Einstein Telescope.