Inter-atomic decay processes are a new class of electronic decay phenomena in clusters, where ionization of one of the cluster units leads to non-radiative decay of the formed vacancy by electron emission from another cluster unit. The first physical phenomenon of this kind, inter-atomic (or inter-molecular) Coulombic decay (ICD) was predicted by Cederbaum and co-workers in 1997 and observed experimentally several years later. Both theoretical and experimental investigations have established ICD as a highly general and a very general decay process. Indeed, ICD is characteristic of vacancy states of van der Waals clusters, hydrogen bonded clusters, and even endohedral fullerenes. The ICD lifetimes were found to belong to the range of 1–100 fs, many orders of magnitude shorter than those of the competing photon emission process. Thus, ICD is the main decay mode of moderate-energy (Auger-inactive) inner shell vacancies in clusters. The mechanism of ICD, rests on the energy transfer between the cluster units at large interatomic distances, amplified by electron cloud overlap at shorter distances. Further inter-atomic decay processes include both energy-transfer-based and electron-transfer-based phenomena. In this talk, I will review the existing variety of inter-atomic decay mechanisms, their theoretical description by means of many-electron theory and outline the perspectives for further development of this field of research.