Financial bubbles are subject to debate and controversy. They are not well understood and are hardly ever characterized specifically, especially ex ante. We define a bubble as a period of unsustainable growth, when the price of an asset increases ever more quickly, in a series of accelerating phases of corrections and rebounds. More technically, during a bubble phase, the price follows a fasterthan- exponential power law growth process, often accompanied by log-periodic oscillations. This dynamic ends abruptly in a change of regime that may be a crash or a substantial correction. In this paper, we will explain the mechanism behind financial bubbles in an intuitive way. We will show how the log-periodic power law emerges spontaneously from the complex system that financial markets are as a consequence of feedback mechanisms, hierarchical structure and specific trading dynamics and investment styles. We argue that the risk of a major correction, or even a crash, becomes substantial when a bubble develops towards maturity, and that it is therefore very important to find evidence of bubbles and to follow their development from as early a stage as possible. We call for the establishment of Financial Crisis Observatories, like the FCO at the ETH Zurich, where financial markets can be monitored continuously for potential systemic risk, and where both generally accepted as well as innovative tools and models can be tested and challenged in a scientific way.