We propose several tests for rational bubbles and investigate their power properties. The focus lies on the case where bubble detection is reduced to testing for a unknown change from a random walk to an explosive process. In simulations, a Chow-type break test exhibits the highest power and performs well relative to the power envelope. The Chow-type procedure also provides a reliable estimator for the break date. Furthermore, we suggest monitoring procedures for detecting speculative bubbles in real time. As applications, we analyze the Nasdaq composite index and various other financial time series.