What are the prospects for conflict and cooperation (and ultimately for war and peace) now that the Cold War has ended? The various theoretical perspectives come up with rather different answers. Waltzian Neorealism diagnoses business as usual: anarchy prevails; states will continue to have to fend for themselves. With the current transition from bipolarity toward multipolarity we must even expect more, not less, international conflict. Liberals are much more optimistic: international institutions and liberal democracy can pave the way for significant progress toward a peaceful world. Constructivists are also optimistic: states can develop cooperative relationships; anarchy is not a given systemic constraint. Cooperative anarchies are thus a possibility. In this article, I argue that there is an important element missing from the current debate about prospects for international conflict and cooperation. That element concerns the nature of contemporary statehood. Internation relations theory has tended to treat states as fixed, ‘like units’.This is the well-known formulation by Kenneth Waltz: ‘so long as anarchy endures, states remain like units’. ‘To call states “like units” is to say that each state is like all other states in being an autonomous political unit’. ‘We abstract from every attribute of states except their capabilities.’ Kenneth N. Waltz, Theory of International Politics (Reading, MA, 1979), pp. 93, 95, 99. They are not, of course, and the difference between the main types of statehood amounts to much more than the variation in capabilities noted by Realists and the absence or presence of liberal democracy as analyzed by liberals. There are three different main types of state in the present international system, and an identification of them is necessary in order to appreciate current and future patterns of cooperation and conflict.