Globular clusters (GCs) are very dense agglomerates of hundreds of thousands stars and they host some of the oldest known stars in our Universe. Their formation is one of the current outstanding problems in astronomy. GCs were traditionally thought to be simple stellar systems, assuming that all the stars within a given cluster were born at the same time and have the same chemical composition. However, already in the ‘70s, light-element abundance variations (e.g. He, C, N, Na, O) within GCs stars were discovered thanks to spectroscopy and photometry. A typical GC optical and near-UV color-magnitude diagram shows discrete multiple sequences at almost any evolutionary stage, which indicate the presence of multiple stellar populations (MPs). This has led to a new paradigm in our understanding of GC formation, which is intimately linked to the formation of stars and the assembly of galaxies. Indeed, GCs were once thought to form in special conditions, only present in the early Universe. The discovery of young GCs, forming in nearby galaxies, has opened a new window on the problem, allowing us to directly search for the origin of MPs. In this talk, I will present an overview of the MPs problem in GCs. I will report on the latest findings from both an observational and theoretical point of view, with a major accent on the discovery of such a phenomenon in young and intermediate age GCs. Finally, open questions and possible ways forward onto the MPs problem will be discussed.