The direct detection of gravitational waves crowns decades of efforts in the modeling of sources and of increasing detectors' sensitivity. With future third-generation Earth-based detectors or space-based observatories, gravitational-wave astronomy will be at its full bloom. Previously brushed-aside questions on environmental or other systematic effects in the generation and propagation of gravitational waves are now begging for a systematic treatment. Here, we study how electromagnetic and gravitational radiation is scattered by a binary system. Scattering cross sections, resonances and the effect of an impinging wave on a gravitational-bound binary are worked out for the first time. The ratio between the scattered-wave amplitude and the incident wave can be of order 10(-5) for known pulsars, bringing this into the realm of future gravitational-wave observatories. For currently realistic distribution of compact-object binaries, the interaction cross section is too small to be of relevance.