Rock debris covers about a third of the total glacier ablation area in High Mountain Asia. Sustained mass loss from these glaciers is causing supraglacial debris layers to expand and thicken. Predicting the evolution of debris-covered glaciers therefore requires including the feedbacks between debris transport, mass balance and ice flow into numerical glacier models. Our simulations of Khumbu Glacier in the Everest region of Nepal demonstrate that the extensive supraglacial debris layer has developed since the Little Ice Age (LIA) approximately 500 years before present. Since the glacier last advanced during the LIA, 34% of the total ice volume has been lost, mainly by surface lowering rather than terminus recession. As the glacier continues to shrink in response to warming air temperatures, at least 8-10% of the glacier volume will be lost by 2100 CE and the debris-covered tongue will detach from the active upper section within the next 150 years. However, although our model captures the important large-scale processes and feedbacks that determine the behaviour of a debris-covered glacier, these simulations underestimated by a factor of three the magnitude of surface change on Khumbu Glacier identified from satellite imagery spanning the last 40 years. This unaccounted-for mass loss—sometimes referred to as the "debris-cover anomaly"—could be due to surface processes that locally enhance ablation including the formation and decay of ice cliffs and supraglacial ponds. Here we explore the role of supraglacial and englacial processes in contributing to the recent acceleration of mass loss from Khumbu Glacier, using our glacier model alongside results from a field monitoring campaign designed to constrain ablation and ice flow processes on high-elevation debris-covered Himalayan glaciers.