Future gravitational wave detectors will map out and characterize every binary
merger in the history of the universe. The possibilities for new and
unexpected scientific discoveries from this wealth of data is staggering, but
hinges crucially on complementary advances in our theoretical understanding of
the nature of gravitational wave sources. However, the path from Einstein's
equation to precision binary dynamics is notoriously difficult, and
conventional methods may not scale to the demands of future detectors. I will
describe our recent efforts in solving the relativistic two-body problem using
modern tools from quantum field theory.