The hydrological characteristics of debris-covered glaciers are known to be fundamentally different from those of clean-ice glaciers, even within the same climatological, geological, and geomorphological setting. Understanding how these characteristics influence the timing and magnitude of meltwater discharge is particularly important for regions where downstream communities rely on this resource for sanitation, irrigation, and hydropower, such as High Mountain Asia. The hydrology of debris-covered glaciers is complex: rugged surface topographies typically route meltwater through compound supraglacial-englacial systems involving both channels and ponds, as well as pathways that remain unknown. Low-gradient tongues that extend several kilometres retard water conveyance and promote englacial storage. Englacial conduits are frequently abandoned and reactivated as water supply changes, new lines of permeability are exploited, and drainage is captured due to high rates of surface and subsurface change. Seasonal influences, such as the monsoon, are superimposed on these distinctive characteristics, reorganising surface and subsurface drainage rapidly from one season to the next. Recent advances in understanding have mostly come from studies aimed at quantifying and describing supraglacial processes; little is known about the subsurface hydrology, particularly the nature (or even existence) of subglacial drainage. In this review, we consider in turn the supraglacial, englacial, subglacial, and proglacial hydrological domains of debris-covered glaciers in High Mountain Asia. We summarise different lines of evidence to establish the current state of knowledge and, in doing so, identify major knowledge gaps. Finally, we use this information to suggest six themes for future hydrological research at High Mountain Asian debris-covered glaciers in order to make timely long-term predictions of changes in the water they supply.