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, as in-depths and details can be found in the referenced papers.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)