A particular relationship with space, usually called territoriality, is one of the essential characteristics of the modern state. This statement was long considered a commonplace. Recent debates, however, have raised new fundamental questions about both space and the state which require a re-examination of both terms, and thus of the connections between them as well. This introduction maps out some of the terminological and theoretical ground for research into these questions. We successively examine the conceptual history of the state, of public administration, and of space, pointing out reifying uses of all three notions which have been repudiated in theoretical debates but remain influential in many historiographical accounts, as well as in popular discourse. We highlight alternative approaches suggested by newer authors. In particular, we describe both the state and administration in terms of assemblages of people, institutions, and objects. Given that this perspective is also used in some current socio-cultural theories of space, we conclude that states and administrations not only exist in space, use space, and create and shape spaces, but that they are themselves spaces and can be analyzed using the methodological tools which apply to spaces of any kind.