The history of grounded ice-sheet extent on the southern Weddell Sea shelf during the Last Glacial Maximum (LGM) and the timing of post-LGM ice-sheet retreat are poorly constrained. Several glaciological models reconstructed widespread grounding and major thickening of the Antarctic Ice Sheet in the Weddell Sea sector at the LGM. In contrast, recently published onshore data and modelling results concluded only very limited LGM-thickening of glaciers and ice streams feeding into the modern Filchner and Ronne ice shelves. These studies concluded that during the LGM ice shelves rather than grounded ice covered the Filchner and Ronne troughs, two deep palaeo-ice stream troughs eroded into the southern Weddell Sea shelf. Here we review previously published and unpublished marine geophysical and geological data from the southern Weddell Sea shelf. The stratigraphy and geometry of reflectors in acoustic sub-bottom profiles are similar to those from other West Antarctic palaeo-ice stream troughs, where grounded ice had advanced to the shelf break at the LGM. Numerous cores from the southern Weddell Sea shelf recovered sequences with properties typical for subglacially deposited tills or subglacially compacted sediments. These data sets give evidence that grounded ice had advanced across the shelf during the past, thereby grounding in even the deepest parts of the Filchner and Ronne troughs. Radiocarbon dates from glaciomarine sediments overlying the subglacial deposits are limited, but indicate that the ice grounding occurred at the LGM and that ice retreat started before w15.1 corrected 14C kyrs before present (BP) on the outer shelf and before w7.7 corrected 14C kyrs BP on the inner shelf, which is broadly synchronous with ice retreat in other Antarctic sectors. The apparent mismatch between the ice-sheet reconstructions from marine and terrestrial data can be attributed to ice streams with very low surface profiles (similar to those of “ice plains”) that had advanced through Filchner Trough and Ronne Trough at the LGM. Considering the global sea-level lowstand of w130 m below present, a low surface slope of the expanded LGM-ice sheet in the southern Weddell Sea can reconcile grounding-line advance to the shelf break with limited thickening of glaciers and ice streams in the hinterland. This scenario implies that ice-sheet growth in the Weddell Sea sector during the LGM and ice-sheet drawdown throughout the last deglaciation could only have made minor contributions to the major global sea-level fluctuations during these times.