Motivated by repeated spikes and crashes during previous decades we investigate whether the heavily financialized market for crude oil has been driven by speculative bubbles. In our theoretical modeling we draw on the convenience yield approach in order to approximate the fundamental value of the oil price. We separate the oil price fundamental from the bubble component by expressing a standard present-value oil price model in state-space form. We then introduce two Markov-regimes into the statespace representation in order to distinguish between two distinct phases in the bubble process, namely one in which the oil price bubble is a stable process and one in which the bubble explodes. We estimate the entire Markov-switching state-space specification using an econometrically robust Bayesian Markov-Chain-Monte-Carlo (MCMC) methodology. Based on inferential techniques designed for statistically separating both Markov-regimes in the bubble process from each other, we find robust evidence for the existence of speculative bubbles in recent oil price dynamics.