Simple models for ruptures along a heterogeneous earthquake fault zone
are studied, focusing on the interplay between the roles of disorder
and dynamical effects. A class of models are found to operate naturall
y at a critical point whose properties yield power-law scaling of eart
hquake statistics. Various dynamical effects can change the behavior t
o a distribution of small events combined with characteristic system s
ize events. The studies employ various analytic methods as well as sim
ulations.