This introduction relates the current options of a global history in music to ‘its various pasts’ in the last half-century: the respective efforts of comparative musicology, ethnomusicology, post-colonial studies, globalisation theory, and sound studies. Of these disciplines and research orientations, comparative musicology has carried the stigma of later rejection (more with regard to its historical thinking than to its psychological and cognitive enquiries), but representatives such as Robert Lachmann were able to connect local studies with profound critical questions about global history. Ethnographic methods have since changed, but there is not a general tendency to exoticise or de-historicise peoples, as can be shown with reference to ethnographic studies of African music. Rather, this research emphasises performance, and the situatedness and contingency of ethnographic knowledge. While modern ethnographic research aims to be participatory, it raises questions of agency and entitlement that are foregrounded in post-colonial studies. One of the contradictions these studies have revealed arises between the need to withdraw from universalist historical schemes designed by the West towards local knowledge and the need to ‘de-centre’ the West by invoking global histories from other sides. Many challenges remain here, especially when it comes to the political goals of re-balancing history. Theories of globalisation have led music research in divergent directions; opinions are still divided over the problem of what drives globalisations in music or what they are supposed to drive. ‘Frictions’ (Anna Tsing) may certainly be observed between conceptions of Western music as it globalises. Sound studies, in turn, seem to offer alternatives to a metropolitan concept of music itself, but nevertheless encourage returns to institutional histories. The author concludes by taking up Philip Bohlman’s formula of a ‘global moment’ of today, which requires its own dialogic approaches and queries, as we continue to work on – and within – a global history of music.