The topset and slope components of aggrading and accreting shelf-margin prisms, and the role of deltas in margin growth, are reviewed. Shelves are constructed by the repeated regressive-transgressive transits of deltas and other shoreline systems on the shelf platform, and when these sediment-delivery systems reach the edge of a preexisting shelf there may be significant accretion of the margin. Regressing deltas/strandplains and transgressing estuaries/barriers can be variably influenced by waves, tides, or river currents, and the presence/distribution of these processes can change in space and time on the shelf platform, and sometimes systematically in cross-shelf transits. The modeled transit time for modern deltas that are able to cross their shelves completely is surprisingly short, usually less than 100 ky. The separation between deltas that are unable or are able to make the entire transit when sea level is rising moderately (2.1 m/ky) allows accommodation-dominated delivery systems (those that require sea-level fall to force the cross-shelf transit) and supply-dominated systems (those that can cross the shelf even with rising sea level) to be distinguished. These end-member systems, in turn, become important in the rationale for arguing a distinction between the conventional falling (lowstand) relative sea-level model for shelf-margin growth and turbidite accumulations, and a model that delivers deepwater sands with normal regression and rising relative sea level at the shelf margin. The differing deepwater architectures for these two models are outlined.