  In this paper we review air shower data related to the mass composition of
cosmic rays above 10$^{15}$ eV. After explaining the basic relations between
air shower observables and the primary mass and energy of cosmic rays, we
present different approaches and results of composition studies with surface
detectors. Furthermore, we discuss measurements of the longitudinal development
of air showers from non-imaging Cherenkov detectors and fluorescence
telescopes. The interpretation of these experimental results in terms of
primary mass is highly susceptible to the theoretical uncertainties of hadronic
interactions in air showers. We nevertheless attempt to calculate the
logarithmic mass from the data using different hadronic interaction models and
to study its energy dependence from 10$^{15}$ to 10$^{20}$ eV.
