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This review presents a general theory of financial crashes and of stock market instabilities that his co-workers and the author have developed over the past seven years. We start by discussing the limitation of standard analyses for characterizing how crashes are special. The study of the frequency distribution of drawdowns, or runs of successive losses shows that large financial crashes are “outliers”: they form a class of their own as can be seen from their statistical signatures. If large financial crashes are “outliers”, they are special and thus require a special explanation, a specific model, a theory of their own. In addition, their special properties may perhaps be used for their prediction. The main mechanisms leading to positive feedbacks, i.e., self-reinforcement, such as imitative behavior and herding between investors are reviewed with many references provided to the relevant literature outside the narrow confine of …