What? Gravitational waves, tiny ripples in space and time, tell the stories of epic astrophysical events often involving the meeting of two black holes. Of particular interest are extreme-mass-ratio inspirals where one black hole is much larger than the other. To detect and interpret these special events, we need highly accurate and realistic models. This project aims to provide these models. Why? Black holes are regions of spacetime where gravity is so strong that nothing can escape and understanding them is the key to many great mysteries in fundamental physics, astrophysics and cosmology. The gravitational waves from extreme-mass-ratio inspirals are expected to carry a wealth of information about the black hole, providing one of the most promising path for advances in black hole physics. How? To model the extreme-mass-ratio inspirals, the project will combine two analytical methods within Einstein's theory of gravity building on the expertise acquired during the applicant’s PhD. These methods are then used to produce the models needed to measure gravitational wave signals from extreme-mass-ratio inspirals with the future detector, LISA, currently under construction.