<p>Earth’s climate is undergoing dramatic warming that is unprecedented in at least the last ~2000 years. Outlets of the Antarctic ice sheet are experiencing dynamic thinning, terminus retreat and mass loss, however, we are currently unable to accurately predict their future response. The drivers and mechanisms responsible for these observed changes can be better understood by studying the behaviour of outlet glaciers in the geological past. Here, I use cosmogenic nuclide surface-exposure dating and numerical glacier modelling to investigate the past configurations and dynamics of Transantarctic Mountain outlet glaciers, in the Ross Sea sector of Antarctica. Numerical modelling was first applied to understand the present-day and past behaviour of Skelton Glacier. A suite of sensitivity experiments reveal that Skelton Glacier is most susceptible to atmospheric temperature through its affect on basal sliding near the groundingline. Under past climates, large changes occurred in the lower reaches of the glacier, with basal sliding and bedrock erosion predicted in the overdeepened basins during both the Pliocene and Quaternary. Skelton Glacier was likely much shorter and thinner during Pliocene interglacials, with warm-based sliding that extended along most of its length. Informed by the glacier modelling, I applied surface-exposure dating to constrain past fluctuations in the geometry of Skelton Glacier. The lower reaches of the glacier were likely thicker at the Last Glacial Maximum (LGM), supporting the idea of buttressing by grounded ice in the Ross Sea during glacial periods. The glacier then thinned to near-modern surface elevations by ~5.8 ka before present (BP). Multiple isotope analysis (²⁶Al-¹⁰Be) and exposure-burial modelling indicates that Skelton Glacier has fluctuated between interglacial and glacial configurations probably at orbital frequencies since the Miocene. These data record a total of >10 Ma of exposure and 2.5 Ma of burial. An unexpected outcome is that the average cosmogenic production rate over this time appears to have been at least twice that of today. The long-term dynamics of Transantarctic Mountain outlet glaciers are further explored at Mackay Glacier. Here, geomorphological evidence reveals that glaciers can both erode and preserve bedrock surfaces during the same glacial episode, with basal erosion controlled primarily by ice thickness. Mackay Glacier likely experienced a widespread erosive regime prior to the Quaternary and a polythermal glacier regime during the LGM. Deglaciation following the LGM is constrained with (¹⁰Be) surface-exposure dating at Mackay Glacier. Samples collected at two nunataks, across four transects, reveal glacier thinning of >260 m between the LGM and ~200 years BP. Ice surface lowering was initially gradual, however an episode of rapid thinning is then recorded at ~6.8 ka BP, during a period of relative climatic and oceanic stability. This accelerated surface lowering occurred at a rate commensurate with modern observations of rapid ice sheet thinning, persisted for at least four centuries, and resulted in >180 m of ice loss. Numerical modelling indicates that ice surface drawdown resulted from ‘marine ice sheet instability’ as the grounding-line retreated through a deep glacial trough on the inner continental-shelf. This research provides new geological constraints and quantitative predictions of the past behaviour of Transantarctic Mountain outlet glaciers. The basal conditions and discharge of these glaciers evolved through the Late Cenozoic in response to climate forcing at orbital timescales, but also to topographically-controlled feedbacks at centennial to millennial timescales. Importantly, under enhanced atmospheric warming, these results imply that such outlet glaciers could experience greater ice loss through increased basal sliding and unstable grounding-line retreat into overdeepened basins.</p>