Until recently, the influence of basal liquid water on the evolution of buried glaciers in Mars' mid latitudes was assumed to be negligible because the latter stages of Mars' Amazonian period (3 Ga to present) have long been thought to have been similarly cold and dry to today. Recent identifications of several landforms interpreted as eskers associated with these young (100s Ma) glaciers calls this assumption into doubt. They indicate basal melting (at least locally and transiently) of their parent glaciers. Although rare, they demonstrate a more complex mid-to-late Amazonian environment than was previously understood. Here, we discuss several open questions posed by the existence of glacier-linked eskers on Mars, including on their global-scale abundance and distribution, the drivers and dynamics of melting and drainage, and the fate of meltwater upon reaching the ice margin. Such questions provide rich opportunities for collaboration between the Mars and Earth cryosphere research communities.