"The age of gravitational wave astronomy will soon be upon us. Initially the most likely sources to be detected by ground-based detectors will be compact binary systems. This project proposes to deepen our understanding of such two-body systems by computing accurate gravitational waveforms from extreme- and intermediate-mass-ratio systems. The latter is expected to be directly observed in the LIGO and VIRGO detectors and having access to accurate waveforms will allow us to perform precision science with the incoming signals. The detailed information revealed by these signals will allow us to test gravity in the strongest-field regimes and provide rich insight into some of the most mysterious objects in the universe, black holes.The approach taken will be to extend existing perturbation theory techniques, with a particular emphasis on using the results to compute the inspiral of a compact object into a black hole. Recent results have shown that the perturbation theory approach is valid over a much wider range of mass-ratios than previously suspected and, as such, perturbation theory results are already having an impact on studies on a wide class of systems within the two-body problem. By making connections with post-Newtonian, numerical relativity and effective-one-body theory perturbation theory has taken centre stage in binary system modeling recently. This project will further these synergies and provide a deep understanding of large-mass-ratio binary systems.Novel approaches to computing inspirals via the so-called `self-force' approach will be developed. In particular, insight coming from University College Dublin via their Green function approach and the deep knowledge at Massachusetts Institute of Technology of the first-order self-force problem will facilitate the development of new methods for computing gravitational wave emission from the systems of physical interest."