The complicated dynamic processes of the Earth system manifest themselves in the form of mass transports, for example resulting from interactions and feedbacks between the solid Earth and its fluid layers, including ocean, atmosphere, cryosphere and hydrosphere. These mass transport signals, covering a wide range of temporal and spatial signals and could originate from natural and anthropogenic climate change processes are observable via contemporary space geodetic sensors. These signals are identified to be critical towards addresses contemporary outstanding scientific questions, including the causes of global sea-level rise, quantifying ice-sheet and glacier mass balance, studying basin-scale hydrology and global water cycle, better understanding of coseismic deformation and geodynamic processes such as the glacial isostatic adjustment. Space geodesy during the onset of the 21st Century is evolving into a transformative cross-disciplinary Earth science discipline. In particular, advances in the measurement of the gravity with modern free-fall methods reached accuracies of 10-9 g (~1 microGal or 10 nm/s2), allowing accurate measurements of height changes at ~3 mm relative to the Earth’s center of mass, and mass transports within the Earth interior or its geophysical fluids, enabling a possible global quantification of climate-change signals. The fundamental mathematical tools to efficiently and accurately exploit and process the big satellite geodetic and remote sensing data sets require addressing fundamental mathematical techniques including boundary value problem, potential theory, adjustment, precision orbit determination, radar physics, and scalable distributed computational algorithms. This presentation summarizes results from the use of data from space gravimetry satellite mission GRACE (Gravity Recovery And Climate Experiment) and other geodetic sensors including satellite altimetry and synthetic aperture radar interferometry (InSAR), to study contemporary scientific problems such as observing and quantifying the causes of 20th and present-day sea-level rise, Earths’ ice and water reservoir mass fluxes, and applications such as timely monitoring of natural hazards such as floods, quantifying world’s water resources, and addressing coastal vulnerability due to sea-level rise.