Observed sequences of large earthquakes are not consistent in either recurrence time or energy release; long-term prediction has been impossible even in areas, such as Parkfield, with well-defined recurrence intervals. The seismic gap hypothesis;which predicts characteristic earthquakes in areas of the circum-Pacific belt that have not produced recent great earthquakes, has also failed to predict the observed clustering of high-energy events. Models in which fractal scaling is broken at high magnitude predict that characteristic events and recurrence behavior will be unstable in time. The central predictions of these models are supported by recent observations at landers and Big Bear in California.