Compact binary systems composed of black holes and neutron stars are among the most promising sources for ground-based gravitational-wave detectors, such as the Laser Interferometer Gravitational Wave Observatory (LIGO) and its international partners. A detailed and accurate understanding of the shape of the gravitational waves is crucial not only for the initial detection of such sources, but also for maximizing the information that can be obtained from the gravitational-wave signals once they are observed. In this talk I will review progresses at the interface between analytical and numerical relativity. These advances have deepened our understanding of the two-body problem in general relativity, revealing an intriguing simplicity and universality of the merger signal of coalescing binary black holes. I will discuss how the effective-one-body approach offers a natural explanation for these results, and explain the importance of accurate modeling for extracting the best science upon detection of gravitational waves.