Cognitive fatigue and boredom are two phenomenological states that reflect overt task disengagement. In this article, we present a rational analysis of the temporal structure of controlled behavior, which provides a formal account of these phenomena. We suggest that in controlling behavior, the brain faces competing behavioral and computational imperatives, and must balance them by tracking their opportunity costs over time. We use this analysis to flesh out previous suggestions that feelings associated with subjective effort, like cognitive fatigue and boredom, are the phenomenological counterparts of these opportunity cost measures, instead of reflecting the depletion of resources as has often been assumed. Specifically, we propose that both fatigue and boredom reflect the competing value of particular options that require foregoing immediate reward but can improve future performance: Fatigue reflects the value of offline computation (internal to the organism) to improve future decisions, while boredom signals the value of exploration (external in the world). We demonstrate that these accounts provide a mechanistically explicit and parsimonious account for a wide array of findings related to cognitive control, integrating and reimagining them under a single, formally rigorous framework. (PsycInfo Database Record (c) 2022 APA, all rights reserved).