The possibility that movements in prices could be due to the self-fulfilling prophecies of market participants has long intrigued observers of free markets. This paper surveys the current state of the empirically-oriented literature concerning rational dynamic indeterminacies, by which we mean a situation of self-fulfilling prophecy within a rational expectations model. Empirical work in this area concentrates primarily on indeterminacies in price levels, exchange rates, and equity prices. We first examine a particular type of explosive indeterminacy, usually called a rational bubble, in an example of the market for equities. Then, we consider empirical work relating to price-level and exchange-rate indeterminacies and empirical studies of indeterminacies in stock prices. Finally, we take up some interpretive issues.