This article develops a ‘spatio-political’ structural typology of (national and international) political systems, based on the arrangement of homogeneous or heterogeneous political centers and peripheries in layered political spaces. I then apply this typology to Eurocentric political systems from the high middle ages to today. Rather than see no fundamental change across nearly a millennium (the system remained anarchic) or a singular modern transition (with several centuries of fundamental structural continuity on either side), I depict a series of partial structural transformations on time scales of a century or two. I also recurrently step back to consider the nature and significance of such structural models; why and how they explain. International systems, I try to show, do not have just one or even only a few simple structures; their parts are arranged (structured) in varied and often complex ways. Structural change therefore is common and typically arises through the interaction and accumulation of changes in intertwined elements of interconnected systems (not from radical innovations or dramatic changes in core principles). And structural models, I argue, explain both continuity and change not by identifying causes (or mechanisms) but through configurations; the organization of the parts of a system into a complex whole.