TTGs (tonalite–trondhjemite–granodiorite) are one of the archetypical lithologies of Archaean cratons. Since their original description in the 1970s, they have been the subject of many studies and discussions relating to Archaean geology. In this paper, we review the ideas, concepts and arguments brought forward in these 40years, and try to address some open questions — both old and new. The late 1960s and the 1970s mark the appearance of “grey gneisses” (TTG) in the scientific literature. During this period, most work was focused on the identification and description of this suite, and the recognition that it is a typical Archaean lithology. TTGs were already recognised as generated by melting of mafic rocks. This was corroborated during the next decade, when detailed geochemical TTG studies allowed us to constrain their petrogenesis (melting of garnet-bearing metamafic rocks), and to conclude that they must have been generated by Archaean geodynamic processes distinct from their modern counterparts. However, the geodynamic debate raged for the following 30years, as many distinct tectonic scenarios can be imagined, all resulting in the melting of mafic rocks in the garnet stability field. The 1990s were dominated by experimental petrology work. A wealth of independent studies demonstrated that melting of amphibolites as well as of mafic eclogites can give rise to TTG liquids; whether amphibolitic or eclogitic conditions are more likely is still an ongoing debate. From 1990s onwards, one of the key questions became the comparison with modern adakites. As originally defined these arc lavas are reasonably close equivalents to Archaean TTGs. Pending issues largely revolve around definitions, as the name TTG has now been applied to most Archaean plutonic rocks, whether sodic or potassic, irrespective of their HREE contents. This leads to a large range of petrogenetic and tectonic scenarios; a fair number of which may well have operated concurrently, but are applicable only to some of the rocks lumped together in the ever-broadening TTG “bin”.