The term grain flow is restricted to sediment gravity flows in which a dispersion of cohesionless grains is maintained against gravity by grain dispersive pressure and in which the fluid interstitial to the grains is the same as the ambient fluid above the flow. Modified flows include those in which a dense interstitial fluid, current, or escaping pure fluid aids in maintaining the dispersion. Conclusions regarding the dynamics of grain flows have been based largely on the analysis of Bagnold (1954) of fully confined, gravity-free dispersions. Natural flows are neither fully confined nor gravity-free, and their characteristics and dynamics differ significantly from his experimental systems. Velocity equations are developed and used to analyze natural grain flows. Unmodified subaerial and subaqueous, steady and uniform flows of sand occur only on slopes at or near the angle of repose, are generally less than 5 cm thick, and cannot individually account for the formation of thick sedimentation units. On slopes inclined at less than the angle of repose, grain flows collapse and freeze; on higher slopes, they accelerate, dilate, and become increasingly influenced by fluid forces. Thick grain flows of gravel-sized debris and thick flows modified by the presence of dense, plastic mud interstitial to the clasts (debris flows), polymodal coarse-sediment size distribution (density-modified grain flows), or concurrent sediment liquefaction or fluidization (liquefied or fluidized sediment flows) can move over relatively low slopes and accumulate as thick sedimentation units.