Recently, there have been numerous great (Mw≥8), devastating earthquakes, with a rate in the last seven years that is 260% of the average rate during the 111‐year seismological history. Each great earthquake presents an opportunity to study a major fault at the very beginning and end of the inferred seismic cycle. In this work, we use these events as both targets and sources to probe susceptibility to dynamic triggering in the epicentral region before and after a large earthquake. This study also carefully addresses the possibility that large earthquakes interact in a cascade of remotely triggered sequences that culminates in further large earthquakes. We seek evidence of triggering associated with the 16 great Mw≥8 events that occurred between 1998 and 2011, using regional and global earthquake catalogs to measure changes in interevent time statistics. Statistical significance is calculated with respect to a nonstationary reference model that includes mainshock–aftershock clustering. We find limited evidence that a few great earthquakes triggered an increase in seismicity at the site of the next great earthquake in the sequence. However, this evidence is not corroborated by all statistical tests nor all earthquake catalogs. Systematic triggered rate changes in the years to decades before each great earthquake are less than 19% at the 95% confidence level, too small to explain the observed rate increase. The catalogs are insufficient for the purpose of resolving more moderate triggering expected from previous studies. We calculate that an improvement in completeness magnitude from 3.7 to 3.5 could resolve the expected triggering signal in the International Seismic Center (ISC) catalog taken as a whole, but an improvement to M 2.0 would be needed to consistently resolve triggering on a regional basis.