This review provides an introduction to the radio emission by particle cascades, an overview on the various experiments, and explains methods for the radio measurement of air-shower properties. Furthermore, potential applications of the radio technique in high-energy astroparticle physics are discussed. Due to the successful operation of digital radio experiments and due to the improved quantitative understanding of the emission, radio detection is back on the list of promising techniques for extensive air showers. With a threshold of about 100 PeV radio detectors are particularly useful to study the highest-energy galactic cosmic rays and ultra-high-energy extragalactic particles of all types. Various antenna arrays like LOPES, CODALEMA, AERA, LOFAR, and Tunka-Rex have shown that radio measurements can compete in precision with other techniques, in particular for the arrival direction, the energy, and the position of the shower maximum. The scientific potential of the radio technique seems to be maximum in combination with particle detectors, which increases the total accuracy for air-shower measurements. This is crucial for a better separation of different primary particles, like gamma-ray photons, neutrinos, or different types of nuclei. In addition to air-showers the radio technique can be used for particle cascades in dense media. Several pioneering experiments like ARA, ARIANNA, and ANITA are currently searching for cascades induced by ultra-high-energy neutrinos in ice. Moreover, several future projects aim at both, high-energy cosmic-rays and neutrinos. SKA will search for neutrino and cosmic-ray initiated cascades in the lunar regolith and provide unprecedented detail for air-shower measurements. Finally, radio detectors with huge exposure like GRAND, SWORD, or EVA are being considered to study the highest energy cosmic rays and neutrinos.
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