Geodesy, the oldest science, has become an important discipline in the geosciences, in large
part by enhancing Global Positioning System (GPS) capabilities over the last 35 years well
beyond the satellite constellation’s original design. The ability of GPS geodesy to estimate
3D positions with millimeter-level precision with respect to a global terrestrial reference
frame has contributed to significant advances in geophysics, seismology, atmospheric science,
hydrology, and natural hazard science. Monitoring the changes in the positions or trajectories
of GPS instruments on the Earth’s land and water surfaces, in the atmosphere, or in space, is
important for both theory and applications, from an improved understanding of tectonic and
magmatic processes to developing systems for mitigating the impact of natural hazards on
society and the environment. Besides accurate positioning, all disturbances in the propagation
of the transmitted GPS radio signals from satellite to receiver are mined for information,
from troposphere and ionosphere delays for weather, climate, and natural hazard applications,
to disturbances in the signals due to multipath reflections from the solid ground, water, and
ice for environmental applications. We review the relevant concepts of geodetic theory, data
analysis, and physical modeling for a myriad of processes at multiple spatial and temporal
scales, and discuss the extensive global infrastructure that has been built to support GPS
geodesy consisting of thousands of continuously operating stations. We also discuss the
integration of heterogeneous and complementary data sets from geodesy, seismology, and
geology, focusing on crustal deformation applications and early warning systems for natural
hazards.