Sedimentary sections up to 6-14 km thick lie beneath many areas of the Antarctic continental margin. The upper parts of the sections contain up to 6 km of Cenozoic glacial and possibly non-glacial sequences that have prograded the continental shelf up to 85 km. We describe the Cenozoic sequences using two general categories based on their acoustic geometries. Type IA sequences, which account for most prograding of the Antarctic continental shelf, have complex sigmoidal geometries and some acoustic characteristics atypical of low-latitude margins, such as troughs and mounds lying parallel and normal to the shelf edge and high velocities (2.0-2.6 km/s) for flat layers within 150 m of the seafloor. Type IIA sequences, which principally aggrade the paleoshelf, lie beneath type IA sequences and have mostly simple geometries and gently dipping reflections. The prograding sequences are commonly located near the seaward edges of major Mesozoic and older margin structures. Relatively rapid Cenozoic subsidence has occured due to the probable rifting in the Ross Sea, thermal subsidence in the Antarctic Peninsula, and isostatic crustal flexure in Wilkes Land. In Prydz Bay and the Weddell Sea, prograding sequences cover Mesozoic basins that have undergone little apparent Cenozoic tectonism. Grounded ice sheets are viewed by us, and others, as the principal mechanism for depositing the Antarctic prograding sequences. During the initial advance of grounded ice the continental shelf is flexurally overdeepened, the inner shelf is heavily eroded, and gently dipping glacial strata are deposited on the shelf (i.e type IIA sequences). The overdeepened shelf profile is preserved (a) during glacial times, by grounded ice sheets episodically crossing the shelf, eroding sediments from onshore and inner shelf areas, and depositing sediments at the front of the ice sheet as outer shelf topset-banks and continental slope foreset-aprons (i.e. type IA sequences), and (b) during interglacial times, like today, by little or no clastic sedimentation on the continental shelf other than beneath retreated ice shelves lying far from the continental sheld edge. Ice streams carve broad depressions across the shelf and carry abundant basal sediments directly to the continental shelf edge, thereby creating troughmouth fans and sheet-like prograding sequences (i.e. type IA sequences). Numerous acoustic unconformities and multiple overcompacted layers within the prograding sequences suggest major fluctuations of the Antarctic Ice Sheet. The available drilling and seismic interpretations provide the following history: (1) Cenozoic ice sheets have existed in places near the continental shelf since middle to late Eocene time. (2) A grounded Antarctic ice sheet first expanded to the continental shelf edge, with probable overdeepening of the outer shelf, in late Eucene to early Oligocene time in Prydz Bay, possibly in early Miocene time in the Ross Sea, and at least by middle Miocene time in the Weddell Sea. (3) The relative amounts of shelf prograding and inferred ice-volume variations (and related sea-level changes) have increased since middle to late Miocene time in the eastern Ross Sea, Prydz Bay, and possibly Weddell Sea. Our analysis is preliminary. Further acoustic surveys and scientific drilling are needed to resolve the proximal Antarctic record of glacio-eustatic, climatic, and tectonic events recorded by the prograding sequences.