Since their theoretical prediction in the late 1990s, inter-atomic Coulombic decay (ICD) and related nonlocal electronic relaxation processes have been in the focus of intensive theoretical and experimental research. The interest was stimulated by their fundamental importance for understanding interatomic electron correlation, relevance for radiation damage in the biochemical matter, and potential for spectroscopic application. The talk will introduce nonlocal decay processes in all the abovementioned contexts, followed by an overview of the current state of their theoretical description. Here, the main focus will be the Fano-ADC method for calculating the decay widths of metastable electronic states.