Behavioral economists have done a great service in connecting psychology and economics. Up to now, however, most have focused on cognitive illusions and anomalies, in order to prove the descriptive failure of neoclassical economic models. Some conjectured that “mental illusions should be considered the rule rather than the exception” (Thaler, 1991, p. 4), thus questioning the assumption that probabilistic judgments are consistent and unbiased. In an influential article, Rabin (1998) concluded: “Because these biases lead people to make errors when attempting to maximize U(x), this research poses a more radical challenge to the economics model” (p. 11). Not everything that looks like a fallacy, however, is one. Economists have been presented a lopsided view of research in psychology (e.g., by Rabin, 1998). Here we explain three of the factors producing the phenomena labeled cognitive illusions: inefficient representations (in the context of base rate fallacy), selected sampling of problems (in the context of overconfidence and availability), and narrow norms (in the context of conjunction fallacy). Understanding these factors allows us to gain theoretical insight into the processes underlying judgment and decision making and to design effective tools to help people reason under uncertainty. We begin with the power of representations. The argument is that the human mind does not work on information, but on representations of information. Many cognitive illusions disappear if one pays attention to this fundamental property of human thinking. For instance, evolved representations of information, such as natural frequencies, promote probabilistic reasoning, whereas conditional probabilities tend to create cognitive illusions. We illustrate the power of representations by demonstrating how one can foster Bayesian reasoning in laypeople and experts.