The era of direct or indirect (ground-based) observations of solar energetic particle (SEP) events covers 50 and 70–80 years, respectively. While thousands of SEP events with soft energy spectra have been recorded directly in space, only about 70 hard-spectrum events detectable at the ground-level (called GLE – ground-level enhancements) have been identified so far, the greatest one being GLE #5 on 23-Feb-1956. Yet, for many practical purposes it is important to know whether the Sun can produce even stronger events, how much stronger, and what the expected rate of their occurrence can be. In order to answer these questions, we need to study much longer time
scales, covering many millennia, which can be done only using data of cosmogenic radionuclides systematically recorded in natural archives. An overview of the today’s knowledge of the extreme SEP events is presented, and assessments of the worst case scenario for the SEP fluence in the vicinity of Earth is made. It is shown that the presently available set of direct data provides insufficient statistic to study extreme events and their occurrence probability distribution. On the other hand, data on cosmogenic radionuclides in terrestrial and lunar samples makes it possible to estimate the probability of extreme events occurrence. It is also shown that the SEP event (or a consequences of events) of 775 AD, identified in cosmogenic data as being a factor 40–50 stronger than the greatest GLE # 5, may serve as a reliable worst-case scenario estimate, but the occurrence rate of such events still remains poorly constratined.