The persistent failure of present-value models to explain asset price levels led academic research to introduce the concept of bubbles as a tool to model price deviations from present value relations. The early literature was dominated by models in which all agents were assumed to be rational and yet a bubble could exist. In many of the more recent papers, the perfect rationality assumption was relaxed, allowing the models to shift the focus to explaining how a bubble may be initiated, under which conditions it would burst, and why arbitrage forces may fail to ensure that prices reflect fundamentals at all times. In light of the recent U.S. real estate bubble, the question of why bubbles are so prevalent is once again a matter of concern for academics and policy makers. This paper surveys the recent literature on asset price bubbles, with significant attention given to behavioral models as well as rational models with incentive problems, market frictions, and non-traditional preferences.