  In this work we review the efforts that have been done to study the
excitation of the standing fast kink body mode in coronal loops. We mainly
focus on the time-dependent problem, which is appropriate to describe flare or
CME induced kink oscillations. The analytical and numerical studies in slab and
cylindrical loop geometries are reviewed. We discuss the results from very
simple one-dimensional models to more realistic (but still simple) loop
configurations. We emphasise how the results of the initial value problem
complement the eigenmode calculations. The possible damping mechanisms of the
kink oscillations are also discussed.
