We explain the multiple populations recently found in the ‘prototype’ globular cluster (GC) NGC 2808 in the framework of the asymptotic giant branch (AGB) scenario. The chemistry of the five – or more – populations is approximately consistent with a sequence of star formation events, starting after the Type II supernova epoch, lasting approximately until the time when the third dredge-up affects the AGB evolution (age ∼90–120 Myr), and ending when the Type Ia supernovae begin exploding in the cluster, eventually clearing it from the gas. The formation of the different populations requires episodes of star formation in AGB gas diluted with different amounts of pristine gas. In the nitrogen-rich, helium-normal population identified in NGC 2808 by the UV Legacy Survey of GCs, the nitrogen increase is due to the third dredge-up in the smallest mass AGB ejecta involved in the star formation of this population. The possibly iron-rich small population in NGC 2808 may be a result of contamination by a single Type Ia supernova. The NGC 2808 case is used to build a general framework to understand the variety of ‘second-generation’ stars observed in GCs. Cluster-to-cluster variations are ascribed to differences in the effects of the many processes and gas sources which may be involved in the formation of the second generation. We discuss an evolutionary scheme, based on pollution by delayed Type II supernovae, which accounts for the properties of s-Fe-anomalous clusters.