Abstract: Despite impressive achievements in the last few years by numerical relativity in modelling the inspiral of two black holes, the extreme mass-ratio limit still remains unreachable by numerical relativity techniques. This regime is important given that supermassive black holes are believed to be present at the center of galaxies, where they are eagerly capturing smaller objects, like stellar-mass black holes. An extreme mass-ratio inspiral can be viewed as the smaller black hole deviating from a geodesic of the spacetime of the supermassive black hole due to the action of its own field, the self-force. In this talk we will introduce novel methods for the calculation of the self-force which are based on the Green function of the wave equation obeyed by field perturbations of the supermassive black hole. We will present a spectroscopy analysis of the Green function on Schwarzschild black hole spacetime, which includes characteristic resonances ('quasinormal modes') and a branch cut in the frequency domain. We will apply this analysis to reveal geometrical properties of wave propagation on a black hole spacetime and to calculate the self-force.