Are there universal laws governing the persistence of weather, and is it possible to predict climate transitions as generated by natural or man-made perturbations? How can one quantify the roller-coaster dynamics of stock markets and anticipate mega-crashes? Can we diagnose the health condition of patients from heartbeat time-series analysis, which may even form the basis for infarct prevention? This book tackles these questions by applying advanced methods from statistical physics and related fields to all types of non-linear dynamics prone to disaster. The transdisciplinary analysis is organized in some dozen review articles written by world-class scientists.