There is abundant evidence that many individuals violate the rationality assumptions routinely made in economics. However, powerful evidence also indicates that violations of individual rationality do not necessarily refute the aggregate predictions of standard economic models that assume full rationality of all agents. Thus, a key question is how the interactions between rational and irrational people shape the aggregate outcome in markets and other institutions. We discuss evidence indicating that strategic complementarity and strategic substitutability are decisive determinants of aggregate outcomes. Under strategic complementarity, a small amount of individual irrationality may lead to large deviations from the aggregate predictions of rational models, whereas a minority of rational agents may suffice to generate aggregate outcomes consistent with the predictions of rational models under strategic substitutability.