  We trace the evolution of research on extreme solar and solar-terrestrial
events from the 1859 Carrington event to the rapid development of the last
twenty years. Our focus is on the largest observed/inferred/theoretical cases
of sunspot groups, flares on the Sun and Sun-like stars, coronal mass
ejections, solar proton events, and geomagnetic storms. The reviewed studies
are based on modern observations, historical or long-term data including the
auroral and cosmogenic radionuclide record, and Kepler observations of Sun-like
stars. We compile a table of 100- and 1000-year events based on occurrence
frequency distributions for the space weather phenomena listed above. Questions
considered include the Sun-like nature of superflare stars and the existence of
impactful but unpredictable solar "black swans" and extreme "dragon king" solar
phenomena that can involve different physics from that operating in events
which are merely large.
