  Inspiralling and coalescing binary black holes are promising sources of
gravitational radiation. The orbital motion and gravitational-wave emission of
such system can be modelled using a variety of approximation schemes and
numerical methods in general relativity: the post-Newtonian formalism, black
hole perturbation theory, numerical relativity simulations, and the effective
one-body model. We review recent work at the multiple interfaces of these
analytical and numerical techniques, emphasizing the use of
coordinate-invariant relationships to perform meaningful comparisons. Such
comparisons provide independent checks of the validity of the various
calculations, they inform the development of a universal, semi-analytical model
of the binary dynamics and gravitational-wave emission, and they help to
delineate the respective domains of validity of each approximation method. For
instance, several recent comparisons suggest that perturbation theory may find
applications in a broader range of physical problems than previously thought,
including the radiative inspiral of intermediate mass-ratio and comparable-mass
black hole binaries.
