  Free fall has signed the greatest markings in the history of physics through
the leaning Pisa tower, the Cambridge apple tree and the Einstein lift. The
perspectives offered by the capture of stars by supermassive black holes are to
be cherished, because the study of the motion of falling stars will constitute
a giant step forward in the understanding of gravitation in the regime of
strong field. After an account on the perception of free fall in ancient times
and on the behaviour of a gravitating mass in Newtonian physics, this chapter
deals with last century debate on the repulsion for a Schwarzschild black hole
and mentions the issue of an infalling particle velocity at the horizon.
Further, black hole perturbations and numerical methods are presented, paving
the way to the introduction of the self-force and other back-action related
methods. The impact of the perturbations on the motion of the falling particle
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; in the latter, the geodesic is conceived in the total
(background plus perturbations) field. Regularisation techniques (mode-sum and
Riemann-Hurwitz $z$ function) intervene to cancel divergencies coming from the
infinitesimal size of the particle. An account is given on the state of the
art, including the last results obtained in this most classical problem,
together with a perspective encompassing future space gravitational wave
interferometry and head-on particle physics experiments. As free fall is
patently non-adiabatic, it requires the most sophisticated techniques for
studying the evolution of the motion. In this scenario, the potential of the
self-consistent approach, by means of which the background geodesic is
continuously corrected by the self-force contribution, is examined.
