Abstract: Surface processes on debris-covered glaciers are governed by a variety of controlling factors including climate, debris load, water bodies, and topography. Currently, we have not achieved a general consensus on the role of supraglacial processes in regulating climate–glacier sensitivity in High Mountain Asia, which is mainly due to a lack of an integrated understanding of glacier surface dynamics as a function of debris properties, mass movement, and ponding. Therefore, further investigations on supraglacial processes is needed in order to provide more accurate assessments of the hydrological cycle, water resources, and natural hazards in the region. Given the scarcity of long-term in situ data and the difficulty of conducting fieldwork on these glaciers, many numerical models have been developed by recent studies. This review summarizes our current knowledge of surface processes on debris-covered glaciers with an emphasis on the related modeling efforts. We present an integrated view on how numerical modeling provide insights into glacier surface ablation, supraglacial debris transport, morphological variation, pond dynamics, and ice-cliff evolution. We also highlight the remote sensing approaches that facilitate modeling, and discuss the limitations of existing models regarding their capabilities to address coupled processes on debris-covered glaciers and suggest research directions.