Prediction of earthquakes and volcanic eruptions has concerned researchers for many decades. Several precursors (e.g. seismic, geodetic, geochemical, geological, atmospheric/ionospheric, geomagnetic, electrical) have been observed shortly before an earthquake or volcanic event. However, no precursor, that can accurately be used for forecasting, has yet been discovered due to the involvement of several complex overlapping and interacting physical and chemical processes. In particular, the non-linearity of actual eruptions or quakes implies a high statistical uncertainty about location of measurement devices. Among geochemical precursors, radon gas in groundwater and soil is considered a notable precursor, used to detect chemical and physical changes during the generation of earthquakes and volcanic events. This article critically reviews progress in radon-based monitoring from the year 2000 onwards and catalogs anomalous radon variations found in groundwater and soils. A future deployment of large sensor networks of 1000-10,000 detectors for radon and also thoron detection would bring a shift in paradigm with respect to long-term earthquake and volcanic monitoring. Such a dense network would enable rapid and precise measurements of radon over large areas resulting in establishing significant and relevant statistical data.