This paper explores the resonant history of gravitational atoms in black hole binaries, focusing on how ultralight bosons interact with rotating black holes and how these interactions affect gravitational wave signals. Rotating black holes can produce superradiant clouds of ultralight bosons, which can resonate with the binary system's orbital motion. These resonances can lead to dramatic changes in the binary's eccentricity and inclination, and can either destroy the cloud or leave an imprint on the binary's orbit. The study considers the nonlinear effects of orbital backreaction and allows for generic eccentric and inclined orbits. The research finds that resonances can "start" or "break" above critical thresholds, leading to different outcomes depending on the binary's initial conditions. The paper also discusses the observational signatures of these resonances, including ionization and changes in the binary's parameters. The results are applied to realistic systems, showing that the cloud can survive until the binary enters the detector's band or be destroyed during a resonance at large separations. The study provides a systematic analysis of resonances for realistic parameters, focusing on intermediate and extreme mass ratios, and highlights the importance of considering nonlinear effects and backreaction in understanding the dynamics of gravitational atoms in binary systems. The paper concludes that resonances can significantly impact the gravitational wave signal and provide valuable insights into the properties of the environment surrounding black holes.This paper explores the resonant history of gravitational atoms in black hole binaries, focusing on how ultralight bosons interact with rotating black holes and how these interactions affect gravitational wave signals. Rotating black holes can produce superradiant clouds of ultralight bosons, which can resonate with the binary system's orbital motion. These resonances can lead to dramatic changes in the binary's eccentricity and inclination, and can either destroy the cloud or leave an imprint on the binary's orbit. The study considers the nonlinear effects of orbital backreaction and allows for generic eccentric and inclined orbits. The research finds that resonances can "start" or "break" above critical thresholds, leading to different outcomes depending on the binary's initial conditions. The paper also discusses the observational signatures of these resonances, including ionization and changes in the binary's parameters. The results are applied to realistic systems, showing that the cloud can survive until the binary enters the detector's band or be destroyed during a resonance at large separations. The study provides a systematic analysis of resonances for realistic parameters, focusing on intermediate and extreme mass ratios, and highlights the importance of considering nonlinear effects and backreaction in understanding the dynamics of gravitational atoms in binary systems. The paper concludes that resonances can significantly impact the gravitational wave signal and provide valuable insights into the properties of the environment surrounding black holes.