Probability weighting has been largely ignored by economics despite abundant evidence that riskattitudes are in fact probability dependent. Probability weighting, however, provides a unifyingaccount of many real-world phenomena that are diffcult to reconcile with expected utility theory,such as the equity premium puzzle, the long-shot bias in betting markets, households'underdiversification and their willingness to buy small-scale insurance at exorbitant prices. Recentfindings suggest that probability dependence is not just a feature of laboratory data but is indeedpresent in financial, insurance and betting markets. Thus, the neglect of probability weightingprevents economists from comprehending important phenomena. In this paper, we discuss thefoundations and economic consequences of probability weighting and offer a practitioner's guideto understanding and modeling probability-dependent risk preferences.