Cosmic rays are relativistic particles that come to the Earth from outer space. Despite a great effort made in both experimental and theoretical research, their origin is still unknown. One of the main keys to understand their nature is the determination of its chemical composition as a function of primary energy. In this paper, we review the measurements of the mass composition above 1015 eV. We first summarize the main aspects of air shower physics that are relevant in composition analyses. We discuss the composition measurements made by using optical, radio, and surface detectors and the limitations imposed by current high-energy hadronic interaction models that are used to interpret the experimental data. We also review the photons and neutrinos searches conducted in different experiments, which, in addition to being important to understand the nature of cosmic rays, can provide relevant information related to the abundance of heavy or light elements in the flux at the highest energies. Finally, we summarize the future composition measurements that are currently being planned or under development.
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