The Sun is the ultimate driver of terrestrial environment. On top of relatively slow changes of solar activity, including the irradiative output, the Sun sporadically produces eruptive events, such as flares, coronal mass ejections, which can strongly affect the Earth’s environment. Solar particle events and severe geomagnetic storms can cause serious hazards to the modern technological society. Direct data from the last decades provide statistic for weak, moderate and strong events, but are insufficient to study extreme events. Some extreme events are known historically, such as the strongest white-light flare and geomagnetic storm of 1859 and a solar particle storm of 774-775 AD. However, it is still unknown whether even stronger events can occur and how often. For example, an analysis of sunlike stars suggests that events several orders of magnitude stronger are still possible on the Sun, but the statistic is debatable. We aim to evaluate, for the first time, the limits of the contemporary Sun in producing extreme events, their energy spectra and occurrence probability, and also to assess their effects. This can only be studied using indirect proxies, such as cosmogenic radionuclides 14C or 10Be, measured in natural dateable archives (tree trunks, ice cores, sediments), where such events may leave clear signatures. Their interpretation requires new sophisticated models of production, transport and deposition of the nuclides, a full re-analysis of the existing datasets, and also involving new precise measurements. We will study extreme events on a long-time scale, focusing on the Holocene (last 12000 years) and extending even further, basing on existing and new measurements of cosmogenic nuclides and models to be developed beyond the present state of the art. A re-analysis of the space-era data will be performed. This Project will lead to a new paradigm of extreme solar/stellar events and results with important impact in multiple areas: solar physics by providing new constraints on energy and distribution of extreme events; geophysics by studying terrestrial impacts; astrobiology by assessing radiation environment at exoplanets; and practical/societal applications by providing quantitative risk assessment of Space Weather hazards.