The observation of gravitational waves by the LIGO/Virgo collaborations has opened a new window onto our Universe, and upcoming experiments promise increasingly precise measurements. In parallel developments, building on the insight that gravity is mediated by a massless spin-2 particle, quantum scattering amplitude methods—originally developed for particle physics—provide a novel framework to study gravity and have already impacted weak-field, fully relativistic predictions for gravitational-wave signals. After outlining the growing need for high-precision analytical predictions in light of current and future gravitational wave observations, we will review the scattering-amplitude-based approach to gravitational wave observables, highlighting both its recent successes and some of the remaining challenges for achieving the accuracy required by the expected experimental data.