Deep-sea sediments play a central role in a wide range of subject areas. A number of important controls on the formation of sedimentary deposits have been studied. However, to date, the impact of submarine landscape geometry as a possible control has received comparatively little attention. This seems to be particularly true for intermediate-scale topographic features such as abyssal hills, knolls and seamounts that can be found in many regions of the global seafloor: recent estimates suggest that in the deep open oceans, away from continental margins, there might be as many as ~ 25 × 106 abyssal hills, knolls and seamounts. Despite this large number very little is known about how they influence environmental complexity and patchiness, biogeochemical fluxes and the formation of sedimentary records. This paper reviews the currently known types of fluid-flow interactions with abyssal hills, knolls and seamounts that could potentially influence the way sediments are formed. The main types of relevant flow components are: quasi-steady to eddying background flow; internal lee and near-inertial waves; barotropic and baroclinic tides; and seamount-trapped waves. Previous studies looking into systematic links between fluid dynamics and sediments at hills, knolls and seamounts are reviewed. Finally, a case study is presented which aims to combine our current knowledge and investigate whether a given combination of recent fluid-flow components leaves a detectable imprint in the recent sediments on and around a short seamount. The main conclusions and implications are as follows. (1) Topographically generated flow-field geometries that are composed of a number of different prevailing fluid-flow components can be reflected and detected in properties of the underlying sediments. (2) Tidal and other higher-frequency (lee-wave, near-inertial) components of deep-ocean currents can be essential for locally driving total current velocities across threshold values for non-deposition/erosion/resuspension of freshly deposited deep-sea sediments. Moreover, there is evidence suggesting that not only maximum current speeds but also intensities of higher-frequency (tidal and/or (near-)inertial) current-direction variability might control sediment dynamics and sediment formation. This relativises the view that current speed is the main, or even only, controlling factor for sediment dynamics and sediment formation. (3) When it comes to the reconstruction of paleo-flows, these findings imply that certain sedimentary records may well reveal more about variability in the higher-frequency flow components than about variability in the basin-scale net flow component that often is the focus of paleoceanographic studies. (4) Single-core paleo-records from hill-, seamount- or similarly controlled sediment deposits may be biased due to the asymmetry of flow fields around these topographic features. To arrive at unbiased paleo-records for non-fluid-dynamic parameters, the influence of the flow-field geometry would have to be removed from the record first. (5) It seems the mechanistic understanding of hill- and seamount-related flow/topography interactions and their links to sediment dynamics is approaching a level that may (a) facilitate improved interpretation of topographically controlled sedimentary paleo-records, (b) help fill in the knowledge gap that exists for functional deep-sea biodiversity at intermediate space scales, and (c) improve predictive capabilities for exploration of economically relevant iron–manganese (Fe–Mn) crusts on seamounts.