In my talk I shall discuss the formulation of the two-body problem in general relativity. The setup is to represent two stars coming in from infinity with asymptotically uniform velocities and with no incoming radiation. In electromagnetic theory, where the field equations are linear, the no incoming radiation condition is fulfilled by selecting the retarded Green’s function. In contrast, in general relativity by reason of the nonlinearity of the Einstein field equations, imposing the no incoming radiation condition requires us to consider a sequence of initial value problems with the initial hypersurfaces tending to the infinite past and to choose appropriately the associated sequence of initial dat. I shall explain how this is to be accomplished. I shall discuss the choice of fluid model which leads to the simplest problem. I shall also discuss the Newtonian limit and what is presently known in this case. Finally, in regard to the relativistic problem, I shall point out what seem to me to be the most fruitful directions of research. http://arxiv. org/find/math-ph/1/au:+Christodoulou_D/0/1/0/all/0/1