  Air shower simulation programs are essential tools for the analysis of data
from cosmic ray experiments and for planning the layout of new detectors. They
are used to estimate the energy and mass of the primary particle. Unfortunately
the model uncertainties translate directly into systematic errors in the energy
and mass determination. Aiming at energies $> 10^{19}$ eV, the models have to
be extrapolated far beyond the energies available at accelerators. On the other
hand, hybrid measurement of ground particle densities and calorimetric shower
energy, as will be provided by the Pierre Auger Observatory, will strongly
constrain shower models. While the main uncertainty of contemporary models
comes from our poor knowledge of the (soft) hadronic interactions at high
energies, also electromagnetic interactions, low-energy hadronic interactions
and the particle transport influence details of the shower development. We
review here the physics processes and some of the computational techniques of
air shower models presently used for highest energies, and discuss the
properties and limitations of the models.
