The Earth's great ice sheets are losing mass at accelerating levels, rising global sea levels and posing a significant problem to society. The ice sheets contain enough water to raise sea level by 65 meters, and are the largest reservoirs of freshwater on the planet. Measurements of current ice sheet mass change are important in order to assess their current contribution to sea level rise, and to constrain future projections. There are three general approaches for measuring the current mass balance of ice sheets: the gravimetric method using time-variable gravity measurements, the altimetric method combining surface elevation change measurements with estimates of the density change, and the mass budget method combining rates of mass input from snow and rain with rates of mass output from meltwater runoff, ice discharge and other processes. In this dissertation, we use multiple independent measurements to assess the current uncertainties in mass balance efforts, and to create new estimates of current ice sheet mass change. We investigate key regions of Antarctica, where changes in the ice sheet velocity structure have led to accelerating mass losses. We compile new assessments of the mass change of the Greenland ice sheet, where increased rates of surface runoff and losses from ice sheet dynamics have dramatically shifted the mass balance regime. The work helps constrain estimation errors from GRACE, provides new constraints to ice sheet and glacial isostatic adjustment models, and helps improve our general understanding of the mechanisms driving current ice sheet mass change.