The Sun is magnetically active and often produces eruptive events on different energetic and temporal scales. Until recently, the upper limit of such events was unknown and believed to be roughly represented by direct instrumental observations. However, two types of extreme events were discovered recently: extreme solar energetic particle events on the multi-millennial time scale and super-flares on sun-like stars. Both discoveries imply that the Sun might rarely produce events, called extreme solar events (ESE), whose energy could be orders of magnitude greater than anything we have observed during recent decades. During the years following these discoveries, great progress has been achieved in collecting observational evidence, uncovering new events, making statistical analyses, and developing theoretical modelling. The ESE paradigm lives and is being developed. On the other hand, many outstanding questions still remain open and new ones emerge. Here we present an overview of the current state of the art and the forming paradigm of ESE from different points of view: solar physics, stellar–solar projections, cosmogenic-isotope data, modelling, historical data, as well as terrestrial, technological and societal effects of ESEs. Special focus is paid to open questions and further developments. This review is based on the joint work of the International Space Science Institute (ISSI) team #510 (2020–2022).
