Why are asset prices so much more volatile and so often detached from their fundamentals? Why does the burst of financial bubbles depress the real economy? This paper addresses these questions by constructing an infinite-horizon heterogeneous-agent general-equilibrium model with speculative bubbles. We show that agents are willing to invest in asset bubbles even though they have positive probability to burst. We prove that any storable goods, regardless of their intrinsic values, may give birth to bubbles with market prices far exceeding their fundamental values. We also show that perceived changes in the bubbles probability to bust can generate boom-bust cycles and produce asset price movements that are many times more volatile than the economy’s fundamentals, as in the data.