Globular clusters in galaxies still challenge astronomers to find a satisfactory explanation for a number of their properties, namely: (i) their very formation; (ii) the origin of their heavy elements; (iii) the trend of their metallicity with distance from the centre of the parent galaxy; (iv) the apparent correlation of their average metallicity with the mass of the galaxy with which they are associated; and, (v) the need of a “second parameter” (age? helium? [CNO/Fe]?) to explain the variety of morphologies of their colour-magnitude diagrams. Dwarf spheroidal galaxies pose similar problems, to an even more puzzling degree. It is clear that an understanding of the above topics is practically the same as the understanding of the very early evolution of galaxies. Any model for the formation and early evolution of galaxies should necessarily be tested whether or not the predicted properties of the associated globular cluster family are in agreement with the observational constraints. Conversely, any attempt to account for the characteristics of globular clusters would be blind without the support of detailed protogalactic models.