More than 100 years after the discovery of cosmic rays we still know little about the origin of the most energetic particles in the universe. These cosmic particles are mainly atomic nuclei which are accelerated by nature to energies far beyond the reach of human-made accelerators. The highest energy particles seem to originate from other galaxies, but neither these extragalactic sources nor the most energetic sources in our galaxy, the Milky Way, are known. To solve these questions, on the one hand, more accurate measurements of the energy-dependent mass composition of the cosmic rays are required. On the other hand, the measurement of neutral particles, i.e., photons and neutrinos, can provide a direct discovery of the sources. In the last years digital antenna arrays have become a competitive alternative for cosmic rays above 10^17 eV. By complementing existing cosmic-ray observatories, antennas can boost the total measurement accuracy. The threshold likely can be lowered to 10^15 eV, which will enable the use of the radio technique for the search for Galactic PeV photons in addition to cosmic-ray measurements. At the same time, radio detectors are the most promising technique for the search for ultra-high-energy neutrinos. ... mehrThis talk will start with an introduction to high-energy astroparticle physics and provide an overview on existing and future radio experiments for cosmic rays and neutrinos.