This paper considers the model of ‘core and periphery,’ widely used in recent decades. It briefly describes the constituent elements of the original model as developed by Immanuel Wallerstein and the manner in which students of the Roman Empire have attempted to apply it. lt begins with a brief discussion of Greek and Roman images of the geography of the world and Roman views of the geography of their empire, to see to what extent this may have influenced modern interpretations, notably those dealing with ‘core and periphery’. My argument is that those who claim to follow Wallerstein in their discussion of ancient empires are using a model that is not suitable for their study of this subject. They therefore rather freely adapt the theory to their needs, without analysing its proper application. The model, it is argued, is mostly inappropriate for the study of ancient empires. When applied, it leads to confusion rather than deeper understanding. Next follows a brief consideration of another model, developed more recently by Peregrine Horden and Nicholas Purcell in their major work The Corrupting Sea. Some possible modifications and additional considerations are suggested. The point of this discussion is to show that there are many instances where Roman administrative arrangements may give a sense of ancient geographical perspective that runs counter to that obtained by looking at modern maps. We are faced with some of the numerous instances of anachronism encountered in modern research.