We hypothesize that the seismicity rate is normally constant. Before and after major earthquakes, the seismicity rate in and near the source volume is often disturbed: Fore- and aftershock sequences are the well known expressions of this, but precursory as well as post-quiescences exist. For the post-main shock quiescence the redistribution of stress due to the main event is the obvious cause, as it is for the aftershocks. Although precursory quiescence and foreshocks are clearly defined in many cases, their cause is not obvious. In some cases they may be explained by precursory aseismic creep. Examples of constant seismicity rate are abundant in deep seismic zones. In 70 seismogenic volumes below 60 km depth of 500 earthquakes each in periods of 8 to 30, we found that the standard deviation was close to that expected from a Poisson distribution. Examples of post-quiescence are found on the San Andreas Fault near Parkfield and along the east coast of Japan, where main shocks of M4.7 and M7.5 were followed by complete absence of earthquakes for several years in neighboring volumes that previously produced large numbers of earthquakes. In the same tectonic provinces precursory seismic quiescence of a few years can be clearly defined for some main shocks, the M6 Coyote Lake and Morgan Hills earthquakes along the Calaveras fault, and the M7.1 off-Sanriku earthquake, Japan. In other tectonic provinces we also found precursory quiescence of several years duration: four out of six main shocks (M5) in Utah and the 1989, M7 Spitak earthquake are recently analyzed examples. Like foreshocks, precursory seismic quiescence is an obvious phenomenon that is however not understood yet.