Paleoseismic studies yield observational data on the temporal and spatial rupture characteristics of moderate to large magnitude earthquakes over multiple rupture cycles. Such data are essential for developing predictive models of earthquakes at scales of time and magnitude that affect society. Therefore, paleoseismic data has been influential in assessing seismic hazard and developing models of fault behavior over multiple earthquake cycles. The models can be loosely categorized as deterministic, variable behavior, and clustered. Deterministic models include fault segmentation, characteristic slip, and time predictable behavior. Non-deterministic models include irregular recurrence, variable slip and variable rupture patterns. Several data sets suggest that ruptures are temporally clustered.