The international system of states displays an inherent drive to territorialize and control ‘empty’ or ‘ungoverned’ spaces. States lay claim to frontier spaces, establish control and defend it against rivals. Territorialization is not a continuous process but occurs in episodes. In this paper I compare two cases, the expansion of the territorial sea and the creation of Marine Protected Areas on the high seas, to advance a twofold argument. First, a territorializing episode occurs a) when states construct a space as empty, b) when there are compelling economic and/or security incentives, and c) when the available technology makes cost-efficient control over the space possible. States take an active role in shaping these conditions, i.e. by deploying securitizing discourses or by commissioning the development of new technologies of control. Second, I argue that there are three systemic root causes of this drive to territorialize empty space: a global system of capitalism demanding the valorisation of unused resources, an international society for which spaces that are outside any kind of state authority are anathema, and modernity which promotes a rule-based international order. Oceanic space has seen a series of these territorializing episodes since the end of the Second World War and provides a richness of empirical details that help to illustrate the argument.