Young and old massive star clusters and their stellar populations - Theoretical challenges for the next decade

Several models presented in the literature compete to explain the origin of multiple stellar populations in globular clusters (GC), but they all fail to reproduce the large variety of present-day characteristics of these systems. In parallel, independent clues on GC early evolution may be derived from observations of young massive clusters (YMC) in the Local Group. But are these two populations of clusters related? And can we reconcile the informations and data concerning GCs and YMCs? Here we summarize some open questions on the nucleosynthetic origin of multiple stellar populations in GCs, on the actual evolution and characteristics of GC low-mass stars, and on early gas expulsion from massive clusters. We propose theoretical paths to be explored in the near future.