Debris-covered glaciers from around the world offer distinct environmental, climatic, and historical conditions from which to study the effects of debris on glacier-ice evolution. A rich literature on debris-covered glaciers exists from decades of field work, laboratory studies, remote-sensing observations, and numerical modeling. In general, the base of knowledge established by studying periglacial, glacial, and paraglacial landforms on Earth has been applied to aid interpretation of ice-rich or ice-remnant landforms on Mars, but research has progressed on both planets. For Mars, the spatial distribution of lobate debris aprons and glacier-like forms, in particular, is critical to constraining past climate conditions when such features were active, reconstructing past ice extent, and estimating the total inventory of buried ice remaining in the mid-latitudes of Mars. This review spans a range of knowledge about debris-covered glaciers on Earth, in order to add context to investigations of dust and debris-covered ice on Mars and to put research on both planets in a perspective aimed at maximizing process-based understanding of glacier evolution. The state of knowledge and some gaps in knowledge on Mars are discussed in relation to possible avenues for future research in how landforms are classified, advances in comparative planetology, and new understanding from future missions. While this review is focused primarily on processes controlling active debris-covered glaciers, a key to understanding glacier change through time is to consider individual landforms in context with the full-system environment in which they are found. For Earth, this includes understanding local and regional controls on current glacier change, and how these processes relate to landform development in the past as well as what may develop in the future. For Mars, this includes evaluating how present-day landforms elucidate past ice activity and environmental conditions during epochs when orbital parameters, climate, and water ice distribution were substantially different.