We review and discuss the process of single-shot helicity-independent all-optical switching of magnetization by which a single suitably-ultrafast excitation, under the right conditions, toggles magnetization from one stable state to another. For almost a decade, this phenomenon was only consistently observed in specific rareearth-transition-metal ferrimagnetic alloys of GdFeCo, but breakthrough experiments in recent years have revealed that the same behavior can be achieved in a wide range of multi-sublattice magnets including TbCo alloys doped with minute amounts of Gd, Gd/Co and Tb/Co synthetic ferrimagnets, and the rare-earth-free Heusler alloy Mn 2 Ru x Ga. Aiming to resolve the conditions that allow switching, a series of experiments have shown that the process in the ferrimagnetic alloys GdFeCo and Mn 2 Ru x Ga is highly sensitive to the pulse duration, starting temperature and the alloy composition. We argue here that the switching displayed by these two very different ferrimagnetic alloys can be generally understood within a single phenomenological framework describing the flow of angular momentum between the constituent sublattices and from the sublattices to the environment. The conditions that facilitate switching stem from the properties of these channels of angular momentum flow in combination with the size of the angular momentum reservoirs. We conclude with providing an outlook in this vibrant research field, with emphasis on the outstanding open questions pertaining to the underlying physics along with noting the advances in exploiting this switching process in technological applications.