The Pliocene-early Pleistocene history of the ancestral Rio Grande and Quaternary history of the Rio Mimbres in the southern Rio Grande rift, New Mexico, illustrate how axial rivers may alternately spill into and subsequently abandon extensional basins. Three types of spillover basins are recognized, based on the angle at which the axial river enters the basin and whether it descends the hanging wall dip slope or footwall scarp to reach the basin floor. In the Mimbres basin type, the axial river enters and flows through the spillover basin nearly parallel to the footwall scarp, resulting in a narrow belt of basin-axis-parallel channel sand bodies located near the footwall scarp. In contrast, an axial river may enter a spillover basin at a high angle to its axis, either descending the hanging wall dip slope (Columbus basin type) or footwall scarp (Tularosa basin type), and construct a fluvial fan, consisting of radiating distributary channels orientated nearly perpendicular to the basin axis. Faulting exerts significant control on river spillover by creating the topographic gaps through which the axial river moves and by terminating spillover by subsequently uplifting or tilting the gap. Spillover may also be autocyclic in origin as a result of aggradation to the level of a pre-existing gap, headward erosion creating and/or intersecting a gap, or simple river avulsion upstream of a gap. Predicting facies architecture in the three types of spillover basins is critical to successful subsurface exploration for hydrocarbon reservoirs, groundwater aquifers or placer mineral deposits.