The early 21st century retreat of Jakobshavn Isbræ into its overdeepened bedrock trough was accompanied by acceleration to unprecedented ice stream speeds. Such dramatic changes suggested the possibility of substantial mass loss over the rest of this century. Here we use a three-dimensional ice sheet model with parameterizations to represent the effects of ice mélange buttressing, crevasse-depth-based calving and submarine melting to adequately reproduce its recent evolution. We are the first study on Jakobshavn Isbræ that solves for three-dimensional ice flow coupled with representations of hydro-fracturing-induced calving and mélange buttressing. Additionally, the model can accurately replicate interannual variations in grounding line and terminus position, including seasonal fluctuations that emerged after arriving at the overdeepened basin and the disappearance of its floating ice shelf. Our simulated ice viscosity variability due to shear margin evolution is particularly important in reproducing the large observed interannual changes in terminus velocity. We use this model to project Jakobshavn's evolution over this century, forced by ocean temperatures from seven Earth system models and surface runoff derived from RACMO, all under the IPCC RCP4.5 climate scenario. In our simulations, Jakobshavn's grounding line continues to retreat ∼18.5 km by the end of this century, leading to a total mass loss of ∼2068 Gt (5.7 mm sea level rise equivalent). Despite the relative success of the model in simulating the recent behavior of the glacier, the model does not simulate winter calving events that have become relatively more important.