From wearable displays to smart watches to in-vehicle infotainment systems, mobile computers are increasingly integrated with our day-to-day activities. Interactions are commonly driven by applications that run in the background and notify users when their attention is needed. In this paper, we argue that existing mobile operating systems should manage user attention as a resource. In contrast to permission-based models that either allow applications to interrupt the user continuously or deny all access, the OS should instead predict the importance and complexity of new interactions and compare the demand for attention to the attention available after accounting for the user's current activities. This will allow the OS to initiate appropriate interactions at the right time using the right modality. We describe one design for such a system, and we outline key challenges that must be met to realize this vision.