  Solar flares and CMEs have a broad range of magnitudes. This review discusses
the possibility of "extreme events," defined as those with magnitudes greater
than have been seen in the existing historical record. For most quantitative
measures, this direct information does not extend more than a century and a
half into the recent past. The magnitude distributions (occurrence frequencies)
of solar events (flares/CMEs) typically decrease with the parameter measured or
inferred (peak flux, mass, energy etc. Flare radiation fluxes tend to follow a
power law slightly flatter than $S^{-2}$, where S represents a peak flux; solar
particle events (SPEs) follow a still flatter power law up to a limiting
magnitude, and then appear to roll over to a steeper distribution, which may
take an exponential form or follow a broken power law. This inference comes
from the terrestrial $^{14}$C record and from the depth dependence of various
radioisotope proxies in the lunar regolith and in meteorites. Recently major
new observational results have impacted our use of the relatively limited
historical record in new ways: the detection of actual events in the $^{14}$C
tree-ring records, and the systematic observations of flares and "superflares"
by the Kepler spacecraft. I discuss how these new findings may affect our
understanding of the distribution function expected for extreme solar events.
