This thesis focuses on modelling the gravitational waves and the relativistic motion associated to Extreme Mass Ratio Inspiral (EMRI) systems. These systems consist of a stellar mass compact object gravitationally captured by a super-massive black hole. In black hole perturbation theory, we further develop a numerical method which computes waveforms generated by a point mass particle orbiting a Schwarzschild black hole. The Regge-Wheeler-Zerilli wave equation is solved in time domain. The gauge invariant solution is related to the polarisation modes, the energy and the angular momentum carried by the gravitational waves. In reaction to the energy and the moment lost, the trajectory is modified all along. In the MiSaTaQuWa formalism, we compute the self-force acting upon a point particle which is initially at rest, and then falling into a Schwarzschild black hole. We show how this quantity is defined in the Regge-Wheeler gauge by using the mode-sum regularisation technique. We take into account the self-force effect on the motion of the particle by using an iterative and osculating orbit method conceived herein. We quantify the orbital deviation with respect to the geodesic motion, but also the perturbed wave forms and the associated radiated energy.
