Many developments in economic theory in the 1970s and 1980s depended on the assumption that economic agents made decisions on the basis of "rational expectations" about economic developments, government action and individual behaviour. These rational expectations are based on experience, but how do economic agents behave in new situations in which previous experience is less useful? The concept of bounded or limited rationality is being developed to analyze behaviour in such situations. In this monograph, the author describes and interprets some of the recent work in the area, especially in statistics and econometrics, and in networks and artificial intelligence. He focuses on a number of examples designed to illustrate the issues involved. He describes two laboratory experiments testing versions of the models and concludes by pointing to some promising applications of the methods surveyed, as well as their limitations.