This chapter surveys the vast literature on initial public offering (IPO) underpricing, focusing on the major theories of underpricing, along with the most relevant empirical findings. These theories, or explanations, are classified into those based on asymmetric information, agency conflicts, behavioral issues, share allocation targets, and institutional arrangements. This last classification has received little attention in the previous couple of decades, although the authors argue that the related fixed-offer price constraint, first proposed as an explanation by Ibbotson (1975), can explain a “core” level of underpricing equal to about one-half to two-thirds of that historically observed, while still assuming that issuing firms seek to maximize offering proceeds net of the spread. In addition, it provides a unifying framework for understanding how, and when, the other explanations can contribute to underpricing beyond this core level.