Abstract Research on summarization has mainly been driven by empirical approaches, crafting systems to perform well on standard datasets with the notion of information Importance remaining latent. We argue that establishing theoretical models of Importance will advance our understanding of the task and help to further improve summarization systems. To this end, we propose simple but rigorous defifi- nitions of several concepts that were previously used only intuitively in summarization: Redundancy, Relevance, and Informativeness. Importance arises as a single quantity naturally unifying these concepts. Additionally, we provide intuitions to interpret the proposed quantities and experiments to demonstrate the potential of the framework to inform and guide subsequent works