The problem of motion in General Relativity has lost its academic status
and become an active research area since the next generation of gravity
wave detectors will rely upon its solution. The difficulties in finding
the full solution stem from the many different scales involved in the
problem: the internal structure (finite size effects), the orbit scale and
the long wavelength of gravitational radiation. In addition, divergences
arise due to the point particle approximation. We will show how ideas
borrowed from effective field theory in particle physics (such as NRQCD
and HQET), can be used to solve the problem of motion in a systematic
fashion, one scale at the time, from a Wilsonian point of view. Moreover,
divergences are naturally handled by dimensional regularization.
Applications include Post-Newtonian corrections to the motion,
gravitational energy flux, absorption, and finite size effects for compact
(BHs or neutron stars) spinning binary systems.