  The two-body problem in General Relativity has been the subject of many
analytical investigations. After reviewing some of the methods used to tackle
this problem (and, more generally, the N-body problem), we focus on a new,
recently introduced approach to the motion and radiation of (comparable mass)
binary systems: the Effective One Body (EOB) formalism. We review the basic
elements of this formalism, and discuss some of its recent developments.
Several recent comparisons between EOB predictions and Numerical Relativity
(NR) simulations have shown the aptitude of the EOB formalism to provide
accurate descriptions of the dynamics and radiation of various binary systems
(comprising black holes or neutron stars) in regimes that are inaccessible to
other analytical approaches (such as the last orbits and the merger of
comparable mass black holes). In synergy with NR simulations, post-Newtonian
(PN) theory and Gravitational Self-Force (GSF) computations, the EOB formalism
is likely to provide an efficient way of computing the very many accurate
template waveforms that are needed for Gravitational Wave (GW) data analysis
purposes.
