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Observational evidence shows that the Greenland Ice Sheet (GrIS) is currently losing mass, and that this mass loss is accelerating. In this dissertation, we look at the representation of GrIS climate in the Community Earth System Model (CESM), in which ice sheet interactions with other parts of the climate system can be consistently resolved. The central metric is the surface mass balance (SMB), as a realistic representation of SMB is a prerequisite for gaining confidence in ice sheet mass loss projections. Our first study investigates the representation of polar snow and firn in CESM. We introduce new parametrizations for fresh snow density and snow compaction and increase the number of snow layers in the model. These model improvements largely resolve issues identified by previous work, including an insufficient refreezing capacity and spurious subsurface melt rates. Our second study concerns spatial resolution. Previous work on regional models has indicated that ~20 km resolution is needed to resolve steep SMB gradients near the GrIS margins, whereas CESM has a nominal resolution of 1° (~100 km). We apply, for the first time, regional grid refinement (55 and 28 km) to the Greenland region using Variable Resolution CESM. We find that although precipitation is greatly improved with enhanced resolution, surface runoff is not. Our third study evaluates the present-day GrIS climate in CESM version 2 (CESM2). We find that CESM2 overestimates the net radiative input at the surface in summer, primarily driven by a low biased albedo, which is compensating for a lack in sensible turbulent heat flux. GrIS ablation zones do not always overlap with that in RACMO2, but the difference in total ablation area is small (-11%). Integrated amounts of SMB components melt, refreezing and runoff are all bracketed by RACMO2 equivalents at the resolutions 11 km (native) and 1 km (statistically down- scaled), indicating a good performance. Our last study explores the future timing of GrIS SMB turning from positive to negative. If such situation would be sustained, the GrIS is bound to disappear since there is no other mass gaining mechanism. We combine CESM2 21st century projections with simulations by the state-of-the-art regional climate model RACMO2. We find a regional Greenland warming threshold of 4.5 ± 0.3 °C, relative to preindustrial conditions. Climate model output from CMIP5 and CMIP6 are used to translate this regional threshold into a global warming threshold for irreversible GrIS mass loss of 2.7 ± 0.2 °C. With our studies we demonstrate the potential of Earth system models (ESMs) for simulating future ice sheet climates and SMB.