The very title of this journal reflects a commonplace in scholarly discourse. We want to understand "Judaism" in the Persian and Graeco-Roman periods: the lives and religion of ancient Jews. Some scholars in recent years have asked whether Ioudaioi and its counterparts in other ancient languages are better rendered "Jews" or "Judaeans" in English. This essay puts that question in a larger frame, by considering first Ioudaismos and then the larger problem of ancient religion. It argues that there was no category of "Judaism" in the Graeco-Roman world, no "religion" too, and that the Ioudaioi were understood until late antiquity as an ethnic group comparable to other ethnic groups, with their distinctive laws, traditions, customs, and God. They were indeed Judaeans.