A wide range of structural, volcanic, and depositional processes produce heterogeneity in alluvial-fan aquifers. This heterogeneity is commonly abrupt, and more importantly, it is directional. Prevalent concepts of scales of heterogeneity and stochastic hydrology emphasize nested or hierarchical aquifer structures that can be represented by stationary models. The argument for stationarity is that heterogeneity becomes homogeneous, or spatially periodic, at some scale. Stationarity may exist in some braided and meandering aquifers, but stationarity is generally not valid for alluvial-fan aquifers, because hierarchical structure is generally present only at the microscopic and partially at the mesoscopic scale. Alluvial fans are directional landforms that extend downdip from a point source. Grain size and bed thickness generally decrease down fan. Abrupt to gradational facies relationships change down fan and may be substantially different in adjacent fans. Hydrogeologic properties, which can vary over 14 orders of magnitude, may parallel the down-fan fining trend or may show a "humped" pattern in a down-fan direction. As fans subside, prograde, and retrograde, a directional aquifer is created whose complex heterogeneities require a directional model. The directional alluvial-fan aquifer is best characterized by three directional scales of heterogeneity (from smallest to largest): (1) within-fan (microscopic scale to facies relationships), (2) between-fan (parallel to depositional and structural strike), and (3) cross-fan (perpendicular to depositional and structural strike). A directional view of heterogeneities in alluvial-fan aquifers is essential for correct site characterization and for design of well networks, aquifer tests, and flow models.