One of the discernible trends in the historiography of recent decades – especially in that which concerns the early modern centuries – has been the emergence of a literature that describes itself as Atlantic History. This paper seeks to identify positive and negative reasons why the once-popular history of exploration and discovery has given way to this new subject, it identifies some fresh meanings that may be drawn from some well-known sources when they are reappraised in an Atlantic context, and it suggests some possibly fruitful lines of enquiry that would lead to a better understanding of how an Atlantic world was fashioned and functioned during the sixteenth, seventeenth and eighteenth centuries. Finally, the paper draws a distinction between Atlantic history and Global history and suggests that the latter is a subject that belongs more properly to the nineteenth and subsequent centuries.