Can you reduce uncertainty by thinking? Intuition suggests that this happens through the elusive process of attention: if we expend mental effort, we can increase the reliability of our sensory data. Models based on “rational inattention” formalize this idea in terms of a trade-off between the costs and benefits of attention. This paper surveys the origin of these models in economics, their connection to rate-distortion theory, and some of their recent applications to psychology and neuroscience. We also report new data from a numerosity judgment task in which we manipulate performance incentives. Consistent with rational inattention, people are able to improve performance on this task when incentivized, in part by increasing the reliability of their sensory data.