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The terrestrial gravity eld uctuates, for example, due to pressure changes in the atmosphere or due to mass redistribution during earthquakes. Today, such gravity uctuations can be observed up to frequencies of a few mHz with superconducting gravimeters. At higher frequencies, they contribute as noise, the so-called Newtonian noise, in the gravitational-wave detectors LIGO and Virgo, potentially limiting their sensitivity between about 10Hz and 30Hz. In addition, it was recently argued that uctuations caused by earthquakes could be detected within seconds by a new generation of gravity gradiometers with a potential application in earthquake early warning. Here we will review our current understanding of terrestrial gravity uctuations above 10mHz. We present the main strategies to reduce gravity noise in gravitational-wave detectors, and discuss the bene ts of using gravity gradiometers with improved sensitivity for earthquake-early- warning systems.