Einstein’s theory of general relativity is famous for its mathematical elegance and equally infamous for its complexity. To date, only a few physically useful exact solutions have been found, all of which are restricted to highly symmetric physical scenarios and none of which describe the generation of gravitational waves. Consequently, approximation methods, such as the post-Newtonian approximation, are instrumental in understanding the highly nonsymmetrical and dynamical spacetimes that occur in the generation of gravitational waves. In this talk, I will introduce post-Newtonian theory and discuss its role in predicting the orbital evolution of highly eccentric gravitational wave sources.