Submarine sediment density flows are one of the most important processes for moving sediment across our planet, yet they are extremely difficult to monitor directly. The speed of long run-out submarine density flows has been measured directly in just five locations worldwide and their sediment concentration has never been measured directly. The only record of most density flows is their sediment deposit. This article summarizes the processes by which density flows deposit sediment and proposes a new single classification for the resulting types of deposit. Colloidal properties of fine cohesive mud ensure that mud deposition is complex, and large volumes of mud can sometimes pond or drain-back for long distances into basinal lows. Deposition of ungraded mud (TE-3) most probably finally results fromen masseconsolidation in relatively thin and dense flows, although initial size sorting of mud indicates earlier stages of dilute and expanded flow. Graded mud (TE-2) and finely laminated mud (TE-1) most probably result from floc settling at lower mud concentrations. Grain-size breaks beneath mud intervals are commonplace, and record bypass of intermediate grain sizes due to colloidal mud behaviour. Planar-laminated (TD) and ripple cross-laminated (TC) non-cohesive silt or fine sand is deposited by dilute flow, and the external deposit shape is consistent with previous models of spatial decelerating (dissipative) dilute flow. A grain-size break beneath the ripple cross-laminated (TC) interval is common, and records a period of sediment reworking (sometimes into dunes) or bypass. Finely planar-laminated sand can be deposited by low-amplitude bed waves in dilute flow (TB-1), but it is most likely to be deposited mainly by high-concentration near-bed layers beneath high-density flows (TB-2). More widely spaced planar lamination (TB-3) occurs beneath massive clean sand (TA), and is also formed by high-density turbidity currents. High-density turbidite deposits (TA, TB-2 and TB-3) have a tabular shape consistent with hindered settling, and are typically overlain by a more extensive drape of low-density turbidite (TD and TC,). This core and drape shape suggests that events sometimes comprise two distinct flow components. Massive clean sand is less commonly depositeden masseby liquefied debris flow (DCS), in which case the clean sand is ungraded or has a patchy grain-size texture. Clean-sand debrites can extend for several tens of kilometres before pinching out abruptly. Up-current transitions suggest that clean-sand debris flows sometimes form via transformation from high-density turbidity currents. Cohesive debris flows can deposit three types of ungraded muddy sand that may contain clasts. Thick cohesive debrites tend to occur in more proximal settings and extend from an initial slope failure. Thinner and highly mobile low-strength cohesive debris flows produce extensive deposits restricted to distal areas. These low-strength debris flows may contain clasts and travel long distances (DM-2), or result from more local flow transformation due to turbulence damping by cohesive mud (DM-1). Mapping of individual flow deposits (beds) emphasizes how a single event can contain several flow types, with transformations between flow types. Flow transformation may be from dilute to dense flow, as well as from dense to dilute flow. Flow state, deposit type and flow transformation are strongly dependent on the volume fraction of cohesive fine mud within a flow. Recent field observations show significant deviations from previous widely cited models, and many hypotheses linking flow type to deposit type are poorly tested. There is much still to learn about these remarkable flows.