  Extreme events, such as rogue waves, earthquakes and stock market crashes,
occur spontaneously in many dynamical systems. Because of their usually adverse
consequences, quantification, prediction and mitigation of extreme events are
highly desirable. Here, we review several aspects of extreme events in
phenomena described by high-dimensional, chaotic dynamical systems. We
specially focus on two pressing aspects of the problem: (i) Mechanisms
underlying the formation of extreme events and (ii) Real-time prediction of
extreme events. For each aspect, we explore methods relying on models, data or
both. We discuss the strengths and limitations of each approach as well as
possible future research directions.
