We use a 3-D higher-order glacier flow model for Vadret da Morteratsch (Engadin, Switzerland) to simulate its strong retreat since the end of the Little Ice Age (LIA) and to project its future disintegration under a warming climate. The flow model, coupled to a 2-D energy balance model, is initialized with the known maximum glacier extent during the LIA and subsequently forced with mean monthly precipitation and temperature records. To correctly reproduce the observed retreat of the glacier front for the period 1864-2010, additional mass balance perturbations are required to account for uncertainties in the initial state, the mass balance model, and climate variations not captured by the ambient meteorological records. Changes in glacier volume and area are in good agreement with additional information from historical topographic maps. Under constant 2001-2010 climate conditions, a strong retreat and mass loss continue and Vadret da Morteratsch disconnects from its main tributary, Vadret Pers, before 2020. The future glacier evolution is analyzed in detail to understand the timing and rate of retreat, and to assess the role of ice dynamics. Assuming a linearly increasing warming of more than 3°C by 2100, only isolated and largely stagnant ice patches remain at high elevation.