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Inspiralling and coalescing binary black holes are promising sources ofgravitational radiation. The orbital motion and gravitational-wave emission ofsuch system can be modelled using a variety of approximation schemes andnumerical methods in general relativity: the post-Newtonian formalism, blackhole perturbation theory, numerical relativity simulations, and the effectiveone-body model. We review recent work at the multiple interfaces of theseanalytical and numerical techniques, emphasizing the use ofcoordinate-invariant relationships to perform meaningful comparisons. Suchcomparisons provide independent checks of the validity of the variouscalculations, they inform the development of a universal, semi-analytical modelof the binary dynamics and gravitational-wave emission, and they help todelineate the respective domains of validity of each approximation method. Forinstance, several recent comparisons suggest that perturbation theory may findapplications in a broader range of physical problems than previously thought,including the radiative inspiral of intermediate mass-ratio and comparable-massblack hole binaries.

The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem