When Homeric heroes think about the meaning of their actions, they expect this to take the form of kleos, 'fame', in a future song. This volume explores the consequences of this mode of thinking in the Iliad in particular, and argues that the form of kleos and the interposition of a gap of time between event and meaning produces widespread effects, not only for the thought and psyche of the heroes, but also for the nature of poetry and Homeric scholarship. Is epic time continuous, perpetuating the fame of the heroes in the flow of poetic tradition, or does a gap intervene to put into doubt the self-identity of meaning and the possibility of memory? This question connects the poetic logic of fame for the heroes and singers of epic to the implicit temporalities of Homeric studies. Alongside the analysis of literary figures from the Iliad, such as narrative, objects and similes, this volume reads modern scholarship on Homer - including oral theory, neoanalysis and traditional referentiality - as forms of reception which have produced distinct responses to the temporality of ancient epic. The participants in epic kleos - heroes, poets and scholars - encounter each other through a tradition that joins the memories and presentiments of a past that did not happen and futures that will never arrive.