Surface meltwater is widespread across many of Antarctica’s ice shelves and can contribute towards ice-shelf instability and potential collapse via hydrofracture or militate against potential ice-shelf instabilities by forming drainage systems that export surface meltwater off the ice-shelf edge. It is crucial, therefore, that water area and volume on Antarctic ice shelves are accurately quantified, and that the ways in which water is stored and transferred across ice-shelf surfaces are understood. This is because the partial or complete removal of ice- shelf areas that actively buttress upstream, grounded ice can lead to increased grounded ice contributions to global mean sea levels. Studying these meltwater systems through fieldwork is time consuming, expensive, and limits the spatial and temporal scale of the study. However, by utilising satellite imagery combined with machine learning methods, vast amounts of data can be processed quickly and cheaply, enabling ice-shelf hydrology to be studied on much greater spatial and temporal scales. This thesis develops novel remote sensing and machine learning methods to identify and track spatial and temporal trends in surface meltwater on Antarctic ice shelves. The first method utilises a normalised difference water index adapted for ice (NDWIice) threshold to track the changing volume and geometry of surface meltwater systems on the Nivlisen Ice Shelf for the 2016/2017 melt season in both Landsat 8 and Sentinel-2 imagery. Results presented for the Nivlisen Ice Shelf show the importance of two linear meltwater systems, which hold 63% of the total meltwater volume at the peak of the melt season. The second method uses machine learning to develop a supervised classifier capable of identifying slush (i.e. saturated firn) and ponded meltwater across all Antarctic ice shelves using Landsat 8 imagery. This classifier is validated by four experts, returning accuracies of 84% for ponded water and 82% for slush, before being applied to the Roi Baudouin Ice Shelf as a case study. Between 2013 and 2020, on average, 64% of the meltwater identified on the Roi Baudouin Ice Shelf is classified as slush. The classifier is then applied across eight Antarctic Peninsula ice shelves for the full Landsat 8 record (2013 to 2021). The resulting dataset revealed high total surface meltwater extents in the 2017/2018 and 2019/2020 melt seasons across much of the west Antarctic Peninsula, and high total surface meltwater extents in 2016/2017 and 2019/2020 across much of the east Antarctic Peninsula. Overall, the methods presented in this thesis provide tools capable of utilising large quantitates of remotely sensed data to accurately map all surface meltwater on Antarctic Ice Shelves. Amongst the results presented, a novel dataset showing the extent of slush across the Antarctic Peninsula shows that a large proportion of the total surface meltwater extent on ice shelves is often occupied by slush. This highlights the need for slush to be considered in future surface mass balance models.