  I review the effective field theory (EFT) description of gravitating compact
objects. The focus is on kinematic regimes where gravity is perturbative, in
particular the adiabatic inspiral phase relevant to gravitational wave
detection. For such configurations, there is a hierarchy of length scales which
all play a role in the dynamics, ranging from the gravitational radius, to the
size of the objects, to their typical orbital separation, and finally the
wavelength of the radiation emitted by the system. To disentangle these scales,
and to achieve manifest power counting in the expansion parameter, it is
necessary to construct a tower of EFTs of gravity, each coupled to distinct
line defect localized degrees of freedom. I describe the relevant effective
theories at each scale as well as the matching between these theories across
each physical threshold. While the main applications of these methods are to
classical dynamics, quantum gravity effects, e.g. Hawking graviton exchange,
can be systematically incorporated if the momentum transfers are small compared
to the Planck mass.
