This paper presents an intertemporal model of growing awareness. It provides a framework for analyzing problems with long time horizons in the presence of growing awareness and awareness of unawareness. The framework generalizes both the standard event-tree framework and the framework from Karni and Vier (2017) of awareness of unawareness. Axioms and a representation are provided along with a recursive formulation of intertemporal utility. This allows for tractable and consistent analysis of intertemporal problems with unawareness.