Understanding earthquake (EQ) recurrence relies on information about the timing and size of past EQ ruptures along a given fault. Knowledge of a fault's rupture history provides valuable information on its potential future behavior, enabling seismic hazard estimates and loss mitigation. Stratigraphic and geomorphic evidence of faulting is used to constrain the recurrence of surface rupturing EQs. Analysis of the latter data sets culminated during the mid-1980s in the formulation of now classical EQ recurrence models, now routinely used to assess seismic hazard. Within the last decade, Light Detection and Ranging (lidar) surveying technology and other high-resolution data sets became increasingly available to tectono-geomorphic studies, promising to contribute to better-informed models of EQ recurrence and slip-accumulation patterns. After reviewing motivation and background, we outline requirements to successfully reconstruct a fault's offset accumulation pattern from geomorphic evidence. We address sources of uncertainty affecting offset measurement and advocate approaches to minimize them. A number of recent studies focus on single-EQ slip distributions and along-fault slip accumulation patterns. We put them in context with paleoseismic studies along the respective faults by comparing coefficients of variation CV for EQ inter-event time and slip-per-event and find that a) single-event offsets vary over a wide range of length-scales and the sources for offset variability differ with length-scale, b) at fault-segment length-scales, single-event offsets are essentially constant, c) along-fault offset accumulation as resolved in the geomorphic record is dominated by essentially same-size, large offset increments, and d) there is generally no one-to-one correlation between the offset accumulation pattern constrained in the geomorphic record and EQ occurrence as identified in the stratigraphic record, revealing the higher resolution and preservation potential of the latter. While slip accumulation along a fault segment may be dominated by repetition of large, nearly constant offset increments, timing of surface-rupture is less regular. (C) 2014 Elsevier B.V. All rights reserved.