The satellite gravimetry mission Gravity Record And Climate Experiment (GRACE), which was operational from 2002 to 2017, and its follow-on mission GRACE-Follow-On (GRACE-FO), which has been active since 2018, revolutionized the observation of temporal changes of the Earth's gravitational field. The measurement data from these missions enable the nuanced quantification of mass redistributions on Earth. Water redistributions between continents and oceans caused by climate change are of particular research interest because of their relevance for mankind. These are, for example, the ice mass changes (IMC) of the ice sheets in Antarctica and Greenland, which this work focuses on. IMC estimates derived from satellite gravimetry data, like from other quantification methods, confirm that both the Greenland Ice Sheet (GIS) and the Antarctic Ice Sheet (AIS) have been losing mass over the last two decades. However, these estimates are subject to large uncertainties, which is particularly the case for the AIS. If the mass balance is obtained from gravimetric observations, a major source of uncertainty is the consideration of effects due to glacial isostatic adjustment (GIA). The uncertainty of the present-day gravitational field changes caused by the isostatic adjustment of the solid Earth to IMC during the last centuries and millennia propagates into estimates of the recent IMC. According to results of the Ice sheet Mass Balance Inter-comparison Exercise (IMBIE), the spread of different modelling results predicting the GIA-induced mass effect in Antarctica is almost as large as the estimated rate of the IMC itself. In Greenland, the spread of the mass effect from different GIA modelling results is approximately 20 % of the rate of IMC. Alternatively, the IMC can be determined using surface elevation changes derived from satellite altimetry observations. In this case, any GIA error hardly affects the results, but there is a significant source of uncertainty in the conversion of volume changes into mass changes. It is possible to combine data from satellite gravimetry and satellite altimetry to jointly estimate IMC and GIA mass effects, e.g. by solving an inverse problem (joint data inversion). This is an alternative to the use of GIA modelling results in processing satellite gravimetry data. Results from data combination methods are not only a means to an end to improve the estimation of IMC. They also can contribute to answer geodynamic questions. However, previous estimation strategies for combining satellite gravimetry and satellite altimetry data are subject to some limitations. Many approaches only allow to estimate GIA in a regional framework and not in global framework. Other approaches strongly depend on a priori information from geophysical modelling which are subject to large uncertainties. Furthermore, limitations are due to processing choices, e.g. the use of deterministic parameters over defined time intervals or, e.g. due to the consideration of errors in the applied data sets. This work investigates advancements of data combination methods that allow to quantify IMC and present-day GIA effects. Specifically, the approaches investigated here combine measured gravitational field changes from satellite gravimetry, measured surface elevation changes from satellite altimetry, modelled surface mass balances from regional climate modelling, and modelled firn thickness changes from firn modelling. This cumulative dissertation comprises three publications that investigated three aspects of data combination approaches. The first publication analysed a regional combination approach in Antarctica and results therein demonstrated a significant dependence of the estimated GIA effect on the input data sets and applied processing choices. A bias correction can significantly reduce an initial bias in the determined GIA effect associated to the spherical harmonic coefficients of degree-1 and c₂₀. However, this bias correction regionally constrains the GIA estimate and prevents to implement such an approach in a global framework. The second publication infers long-term mass trends with their temporal changes jointly observed from satellite gravimetry and satellite altimetry data. To do so, a state-space filtering framework was applied to the data sets allowing to estimate temporal changes of the parameters over time while accounting for temporal correlation of short-term fluctuations. Thereby, an accelerating ice-dynamically induced ice mass loss is found for drainage basins in West Antarctica. In contrast, the temporal variability of long-term trends in East Antarctica is low. Noteworthy, the trends in Dronning Maud Land and Enderby Land are positive. The third publication presents a global approach to jointly estimate IMC, GIA effects and firn thickness changes, while accounting for spatial error covariances of the input data sets. The intention of the utilized GIA parametrization in Antarctica is to spatially resolve GIA effects that were not predicted by GIA models. Simulation experiments demonstrated the feasibility of the approach under the presence of realistic limitations of satellite observations and model products. This framework paper also reports a first application of the inversion method of Publication 3 to real data. The focus of this application is on Antarctcia over the time interval January 2011 to December 2020. Results for the AIS are: (i) an IMC of (−150 ± 5) Gt a⁻¹, (ii) a change of the firn air content of (40 ± 5) km³ a⁻¹, and (iii) an integrated GIA-induced mass effect of (72 ± 4) Gt a⁻¹. These results are promising with regard to the application of this methodology, as they are similar to previously published estimates. But they are estimated in a globally consistent framework and without applying conventional filtering strategies. Future work should further improve the methodology and eventually implement it in a global inversion framework that allows to jointly estimate all sea-level contributions.