[en] The status of our knowledge on the mechanisms of multiple captures by a highly charged ion colliding with an atom is reviewed. The various and complementary techniques are first described, including energy gain spectroscopy, electron and photon spectroscopy with a particular emphasis on the rapidly developing techniques combining these spectroscopies in coincidence experiments. The double capture processes are simple enough to allow theoretical calculations and a detailed analysis of capture mechanisms such as the relative role of the electron-nucleus interaction and the electron-electron interaction. This is not yet the case for multiple captures, which imply a very large number of channels. However the simple classical overbarrier model, in its extended form, is able to account for the gross features of multiple capture processes such as the number of electrons stripped from the target. However, such models are often unable to predict the number of electrons actually captured by the projectile. (Author)