Neutrino geophysics, the study of the Earth's interior by measuring the fluxes of geologically produced neutrino at its surface, is a new interdisciplinary field of science, rapidly developing as a synergy between geology, geophysics and particle physics. Geoneutrinos, antineutrinos from longlived natural isotopes responsible for the radiogenic heat flux, provide valuable information for the chemical composition models of the Earth. The calculations of the expected geoneutrino signal are discussed, together with experimental aspects of geoneutrino detection, including the description of possible backgrounds and methods for their suppression. At present, only two detectors, Borexino and KamLAND, have reached sensitivity to the geoneutrino. The experiments accumulated a set of ∼190 geoneutrino events and continue the data acquisition. The detailed description of the experiments, their results on geoneutrino detection, and impact on geophysics are presented. The start of operation of other detectors sensitive to geoneutrinos is planned for the near future: the SNO+ detector is being filled with liquid scintillator, and the biggest ever 20 kt JUNO detector is under construction. A review of the physics potential of these experiments with respect to the geoneutrino studies, along with other proposals, is presented. New ideas and methods for geoneutrino detection are reviewed.