The concept of sediment waves is reviewed and clarifications are proposed for nomenclature concerning vertical channel responses to large fluvial sediment fluxes over a period of a decade or longer. Gilbert’s (1917) original sediment waves are re-evaluated at their type locale and used to develop a consistent set of definitions. A ‘sediment wave’ represents a transient sediment flux that includes but is not necessarily identical to a ‘channel bed wave’ that represents the rise and fall of the bed in response to sedimentation. A large-scale sediment wave results when a major sediment-delivery event generates an aggradation–degradation episode (ADE). It may leave a legacy of sediment deposited on valley bottoms. Gilbert’s classic sediment-wave model was empirically based on changes in bed elevations but was described as a sediment flux. He described downstream translation of an attenuating symmetrical wave although it was too large and disjointed to have a coherent waveform. Rapid return of bed elevations to pre-sedimentation levels in Gilbert’s wave should not be mistaken for exhaustion of sediment. The common concept of a symmetrical sediment wave representing the time series of sediment loads is not accurate for large-scale sedimentation events that store and slowly release sediment on floodplains. Large sediment waves composed of relatively fine material and limited bed armoring tend to be right-skewed owing to rapid vertical readjustments relative to slow lateral recruitment of stored sediment. A revised right-skewed conceptual model of large sediment and bed waves is presented that fits modern observations and incorporates stochastic elements of flood events. Large sediment waves may be linked to legacy sediment; that is, large repositories of anthropogenic alluvium stored on valley bottom floodplains, wetlands, mill ponds, and reservoirs. This illustrates the ubiquity and importance of secular sediment waves to river management.