Cultural historical research has deliberately challenged "historical realism," the view that history is comprised entirely of observable actions that actually occurred, and instead has emphasized the historical significance of thoughts, emotions, and representations; it has also focused on the invisible, the momentary, and the perishable. These latter elements introduce the notion of the possible in history. This article examines the ways in which cultural history has approached the notion of the possible, as well as the methodological and theoretical implications of this approach. Its chief claim is that the idea of possibility is fundamental for the concept of culture and ineliminable from its historical study. The question of possibility is present in multiple ways in the study of history; it is important to distinguish among different levels of possibility. The possible may mean, for instance, what it is possible for historians to know about the past, or the possibilities open to historical agents themselves, or, indeed, the possibilities they perceived themselves as having even if these seem impossible from the point of view of the historian. The article starts with the first aspect and moves on toward the possibilities that existed in the past world either in fact or in the minds of those in the past. The article argues that the study of past cultures always entails the mapping of past possibilities. The first strand of the essay builds on the metaphor of the black hole and intends to solve one of the central problems faced by cultural historians, namely, how to access the horizon of the people of the past, their experience of their own time, especially when the sources remain silent. The second, more speculative strand builds on the notion of plenitude and is designed to open up avenues for further discussion about the concept of culture in particular.