Over the last twenty years, global history has experienced a considerable boom, breaking with traditional historical approaches that privileged the national framework and very often adopted a Eurocentric perspective. This triumphalist discourse about the field of global history should not, however, obscure the local and national specificities of this field of research, be they epistemological, institutional, thematic, or historiographical, nor the disciplinary, political, and economic obstacles with which researchers are confronted. This conversation explores the intellectual and structural specificities and constraints of global history.