In the first part of my talk, I give an overview of some recent results concerning the two-body problem in general relativity at high post-Newtonian (PN) order. I will present the energy flux at 4.5PN order, the equations of motion at 4.5PN order, and the memory contributions to the 3.5PN order waveform. In particular, I will discuss some subtleties about the definition of the center-of-mass frame, and its relevance to the comparison with second-order self-force (2SF) results.