In recent years, historians have debated the prospect of offering new ‘transnational’ or ‘global’ perspectives in their studies. This paper introduces the reader to this special issue by analysing characteristics, merits and flaws of these approaches. It then considers how historians of science have practised transnational history without, however, paying sufficient attention to the theoretical foundations of this approach. Its final part illustrates what benefits may derive from the application of transnational history in the field. In particular, we suggest looking at the construction of transnational networks in science, and discuss some of the methodological consequences of adopting this approach.