Extremal events play an increasingly important role in stochastic modelling in insurance and finance. Over many years, probabilists and statisticians have developed techniques for the description, analysis and prediction of such events. In the present paper, we review the relevant theory which may also be used in the wider context of Operation Research. Various applications from the field of insurance and finance are discussed. Via an extensive list of references, the reader is guided towards further material related to the above problem areas.

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