 This paper reviews the work done by a team of European and American researchers over a three-year period on extreme events, their causes and consequences. It focuses on both theoretical aspects of time series analysis and extreme value theory, as well as the deterministic modeling of extreme events through continuous and discrete dynamic models. Applications include climatic, seismic and socioeconomic events, along with their prediction. Two key findings are that spectral analysis of a time series can be used to identify both the continuous and discrete parts of its power spectrum, and that coupled modeling of natural and socioeconomic systems is necessary to understand and predict the effects of extreme events. These findings have implications for the study and prediction of natural hazards and their human impacts. This article was authored by M. Gil, P. U., S. Halligat and others.