  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 $10^{15}$ 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.
