We investigate the impact of variations in the friction and geometry on models of fault dynamics. We focus primarily on a three-dimensional continuum model with scalar displacements. Slip occurs on an embedded two-dimensional planar interface. Friction is characterized by a two-parameter rate and state law, incorporating a characteristic length for weakening, a characteristic time for healing, and a velocity-weakening steady state. As the friction parameters are varied, there is a crossover from narrow, self-healing slip pulses to crack-like solutions that heal in response to edge effects. For repeated ruptures the crack-like regime exhibits periodic or aperiodic systemwide events. The self-healing regime exhibits dynamical complexity and a broad distribution of rupture areas. The behavior can also change from periodicity or quasi-periodicity to dynamical complexity as the total fault size or the length-to-width ratio is increased. Our results for the continuum model agree qualitatively with analogous results obtained for a one-dimensional Burridge-Knopoff model in which radiation effects are approximated by viscous dissipation. ¿ 2000 American Geophysical Union