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Abstract. Modern concept of Extreme Solar Event (ESE) is critically analyzed based on available direct and proxy data on solar cosmic rays (SCR), or solar energetic particles (SEP). Special attention is paid to recent debate on validity, origin and properties of the events AD1859 (Carrington event, CE) by nitrate method and AD775 by radionuclide data. We demonstrate that, in spite of existing uncertainties in proton fluences above 30 MeV, all of them are fitted well by a unique distribution function, at least, with present level of solar activity. Extremely large SEP fluxes are shown to obey a probabilistic distribution with a sharp break in the range of large fluences (or low probabilities). The studies of this kind may be extended for the periods with different levels of solar activity in the past and/or in the future. Considering the recent confirmation of super-flares on solar-type stars, this issue merits attention.