Rogue waves in the sea: observations, physics, and mathematics

Rogue waves are anomalously high waves that may suddenly form on the sea surface. At the dawn of the 21st century, they attracted the interest of researchers, from oceanographers to mathematicians. The review discusses the results of their research: physical mechanisms leading to the generation of anomalously high waves and respective mathematical models, observational data, results of direct numerical simulations and laboratory experiments, and new approaches to modeling and forecasting extreme sea waves.