Terrestrial cosmogenic nuclides (e.g., 14C, 10Be, and 36Cl) are primarily produced by galactic cosmic rays. However, a certain amount of these nuclides is also produced by solar energetic particles (SEPs) derived from sporadic solar events such as solar flares and coronal mass ejections. Cosmic ray increase events in AD 774/775, AD 993/994 (or AD 992/993), and ~BC 660 have been discovered using 14C data in tree rings (Miyake et al. 2012, 2013; Park et al. 2017). It is considered that the most plausible cause of these events was an extreme SEP events with very hard energy spectra based on 14C analyses of tree rings and 10Be and 36Cl analyses of ice cores (e.g., Mekhaldi et al. 2015; Miyake et al. 2015, 2019; Büntgen et al. 2018; O'Hare et al. 2019). These SEP events are estimated to be several dozens of times larger than the largest events seen in direct observations, and an event of that size might have a serious impact on modern society. Therefore, it is important to investigate the occurrence rate of past extreme events. In recent years, surveys of past SEP events have been actively conducted via cosmogenic nuclide measurements with high time resolution (~one-year resolution). Here the detected past SEP candidates and a further survey of similar events are reviewed.