The two-body problem in general relativity has been the focus of intense observational and theoretical interest in recent years, especially as gravitational-wave astronomy has begun delivering on its long promised potential. A wide variety of approaches, valid in different regimes, have been used to understand the dynamics of binaries: numerical relativity, the post-Newtonian approximation, the post-Minkowskian approximation, the small mass ratio approximation, and the effective one-body framework, which synthesizes information from the other approaches. The success of future gravitational wave observations (both future ground and space based) depends on our ability to model the fundamental physics of two-body systems and produce accurate waveform templates that are used in the matched filtering techniques that these observatories employ. An issue that arises in the study of two-body systems is whether one can define dissipative and conservative sectors of the dynamics for which the conservative sector admits a Hamiltonian description. Such a description would unlock the full power of Hamiltonian methods to study integrability and chaotic motion, obtain new gauge invariant quantities and better understand the effect of resonant orbits. In this thesis, we show that such dissipative and conservative sectors can be defined in the limit where one of the bodies is much smaller than the other, and derive a Hamiltonian description to linear order in the mass and spin of the secondary. We also extend this result to second order, in the context of a scalar toy model of the gravitational interaction. In deriving these results, we develop two useful theoretical tools. First, we show that abroad class of dynamical systems, defined by non-local in time action principles, can be recast as local Hamiltonian systems to all orders in the non-locality. Second, we develop a reformulation of the dynamics of bodies with strong self-interactions which shows that their motion is equivalent to that of bodies with negligible self-interactions, albeit in a renormalized or effective external field.