The possibility that movements in market prices of assets or goods may be caused by self-fulfilling prophecies, called bubbles or sunspots, has long intrigued market observers. If bubbles or sunspots exist, market prices differ from their fundamental values, and markets do not necessarily allocate resources to their best possible uses. Some might argue then that public policies would be needed to alleviate such problems. 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. The 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 a familiar model of equity pricing. We then consider empirical work relating to price level and exchange rate indeterminacies, before examining empirical studies of indeterminacies in stock prices. Finally, we take up some interpretive issues. We find that existing bubbles tests do not establish that rational bubbles exist in asset prices.