Bad decisions can have devastating consequences: There is a vast body of literature claiming that human judgment and decision-making are riddled with numerous systematic violations of the rules of logic, probability theory, and expected utility theory. The discovery of these cognitive biases in the 1970s (Tversky & Kahneman, 1974) made people question the concept of Homo sapiens as the rational animal, profoundly shaking the foundations of economics and rational models in the cognitive, neural, and social sciences. Four decades later, these disciplines still lack a rigorous theoretical foundation for explaining and remedying people’s cognitive biases. To solve this problem, my dissertation offers a mathematically precise theory of bounded rationality and demonstrates how it can be leveraged to elucidate the cognitive mechanisms of judgment and decision-making (Part 1) and to help people make better decisions (Part 2).