Chemical and physical Earth models agree little as to the radioactive power of the planet. Each predicts a range of radioactive powers, overlapping slightly with the other at about 24 TW, and together spanning 14–46 TW. Approximately 20% of this radioactive power (3–8 TW) escapes to space in the form of geoneutrinos. The remaining 11–38 TW heats the planet with significant geodynamical consequences, appearing as the radiogenic component of the 43–49 TW surface heat flow. The nonradiogenic component of the surface heat flow (5–38 TW) is presumably primordial, a legacy of the formation and early evolution of the planet. A constraining measurement of radiogenic heating provides insights to the thermal history of the Earth and potentially discriminates chemical and physical Earth models. Radiogenic heating in the planet primarily springs from unstable nuclides of uranium, thorium, and potassium. The paths to their stable daughter nuclides include nuclear beta decays, producing geoneutrinos. Large subsurface detectors efficiently record the energy but not the direction of the infrequent interactions of the highest‐energy geoneutrinos, originating only from uranium and thorium. The measured energy spectrum of the interactions estimates the relative amounts of these heat‐producing elements, while the intensity estimates planetary radiogenic power. Recent geoneutrino observations in Japan and Italy find consistent values of radiogenic heating. The combined result mildly excludes the lowest model values of radiogenic heating and, assuming whole mantle convection, identifies primordial heat loss. Future observations have the potential to measure radiogenic heating with better precision, further constraining geological models and the thermal evolution of the Earth. This review presents the science and status of geoneutrino observations and the prospects for measuring the radioactive power of the planet. Key Points Radiogenic heating and geoneutrino flux are closely related Earth models predict measurably distinct radioactive heat and geoneutrino flux Oceanic geoneutrino measurement allows resolution of Earth radioactive power