This article proposes an infinite hidden Markov model (iHMM) to detect, date stamp, and estimate speculative bubbles. Three features make this new approach attractive to practitioners. First, the iHMM is capable of capturing the complex nonlinear dynamics of bubble behaviors because it allows for an infinite number of regimes. Second, implementing this procedure is straightforward because bubbles are detected, dated, and estimated simultaneously in a coherent Bayesian framework. Third, because the iHMM assumes hierarchical structures, it is parsimonious and superior in out-of-sample forecasts. This model and extensions of this model are applied to the NASDAQ stock market. The in-sample posterior analysis and out-of-sample predictions find evidence of explosive dynamics during the dot-com bubble period. A model comparison shows that the iHMMis strongly supported by the data compared with finite hidden Markov models.