Phenomenology of cosmic ray air showers

The properties of cosmic rays with energies above 1PeV have to be deduced from the spacetime structure and particle content of the air showers which they initiate. In this review, a summary of the phenomenology of these giant air showers is presented. We describe the hadronic interaction models used to extrapolate results from collider data to ultra high energies, an also the main electromagnetic processes that govern the longitudinal shower evolution as well as the lateral spread of particles.