Glacier mass loss is an iconic process induced by anthropogenic climate change. It threatens human livelihood at coasts affected by the rising sea level and in glacierized hydrological basins where the glacial runoff is essential for water availability. Moreover, as glacier mass loss adds large amounts of freshwater to the oceans, it might alter ocean circulation in a way that affects marine ecosystems and the climate system. Only recently, satellite-data processing revealed mass changes on an individual glacier level (outside the large ice sheets), but only for the last two decades. Glacier mass change observations become increasingly sparse going back in time. Therefore, the glaciers' past contribution to global mean sea level rise can only be reconstructed using numerical models. Since glacier mass change will continue during this century, it is vital to understand how this will affect global mean sea level, ocean circulation, and regional hydrology. Again, this is only possible using numerical models. Hence, it is essential to improve these models by incorporating previously neglected processes of glacier mass change into them, mainly in the form of parametrizations, and by constraining them using observations. Moreover, it is crucial to understand the uncertainties of results produced by numerical models, as they can never fully represent the natural world, which also hinges on the amount and quality of observational data. This work will tackle aspects of three issues in numerically modeling glacier mass changes: past glacier mass change reconstructions' uncertainties, future mass change projections' uncertainties, specifically regarding marine-terminating glaciers, and ice-ocean interactions in the northern hemisphere outside the Greenland ice sheet. All three issues are relevant in addressing the question of how glaciers respond to changes in their mass balance due to climatic changes and what consequences such changes have for the Earth system and, ultimately, human livelihood. It is found that the further outside the glaciological and meteorological observations' spatial and temporal domain a numerical model is applied, the more uncertain reconstructed glacier mass changes become. Similarly, one primary source of uncertainty in future glacier mass change projections is the difference in climate models' outputs of near-surface temperatures and precipitation. More accurately describing marine-terminating glacier dynamics and considering volume changes below sea level reduces estimates of future glacier contribution to global mean sea level rise systematically. However, significant uncertainties due to uncertainty about appropriate values for parameters involved in modeling (marine-terminating) glaciers' dynamics are detected. Concerning ice-ocean interactions, it was found that including the freshwater input from glacier mass loss in the northern hemisphere (outside the Greenland ice sheet) in an ocean general circulation model significantly impacts the simulated high-latitude ocean circulation. Finally, a first estimate of the ice mass glaciers lose due to melting directly into the ocean was produced.