  Through detection by low gravitational wave space interferometers, the
capture of stars by supermassive black holes will constitute a giant step
forward in the understanding of gravitation in strong field. The impact of the
perturbations on the motion of the star is computed via the tail, the
back-scattered part of the perturbations, or via a radiative Green function. In
the former approach, the self-force acts upon the background geodesic, while in
the latter, the geodesic is conceived in the total (background plus
perturbations) field. Regularisations (mode-sum and Riemann-Hurwitz $\zeta$
function) intervene to cancel divergencies coming from the infinitesimal size
of the particle. The non-adiabatic trajectories require the most sophisticated
techniques for studying the evolution of the motion, like the self-consistent
approach.
