  In this short review we present a self-contained exposition of the effective
field theory method approach to model the dynamics of gravitationally bound
compact binary systems within the post-Newtonian approximation to General
Relativity. Applications of this approach to the conservative sector, as well
as to the radiation emission by the binary system are discussed in their
salient features. Most important results are discussed in a pedagogical way, as
in-depths and details can be found in the referenced papers.
