Abstract: In February 2018, we hosted a workshop on Antarctic Surface Hydrology and Future Ice-shelf Stability at Lamont-Doherty Earth Observatory, Palisades, New York. Funding for the workshop was provided by the U.S. National Science Foundation (NSF) Antarctic Glaciology Program (award number: 1743326). The aims of the workshop were to: (1) establish the state-of-the-science of Antarctic surface hydrology; (2) identify key science questions raised by observations and theoretical studies of Antarctic surface hydrology, and (3) move the community toward answering these questions by bringing together scientists with diverse expertise. The workshop was motivated by the premise that significant gains in our understanding can be made if researchers with interests in this field are provided with an opportunity to communicate and develop collaborations across disciplines. Here we report on the organisation, attendance, and structure of the workshop, before summarizing key science outcomes, research questions, and future priorities that emerged during the workshop within the following four themes: 1. Surface melting: controls and observations 2. Water ponding and flow 3. Impact of meltwater on ice-shelf stability 4. Ice-sheet/climate modeling Finally, building on the emergent science questions, we propose a framework for prioritizing future work, aimed at understanding and predicting the impact that surface meltwater will have on future Antarctic Ice Sheet mass balance.