  In this report we review the important progress made in recent years towards
understanding the experimental data on ultra-high-energy ($E \gtrsim 10^9$ GeV)
cosmic rays. We begin with a general survey of the available data, including a
description of the energy spectrum, the nuclear composition, and the
distribution of arrival directions. At this point we also give a synopsis of
experimental techniques. After that, we introduce the fundamentals of cosmic
ray acceleration and energy loss during propagation, with a view of discussing
the conjectured nearby sources. Next, we survey the state of the art regarding
the high- and ultra-high-energy cosmic neutrinos which may be produced in
association with the observed cosmic rays. These neutrinos could constitute key
messengers identifying currently unknown cosmic accelerators, possibly in the
distant universe, because their propagation is not influenced by background
photon or magnetic fields. Subsequently, we summarize the phenomenology of
cosmic ray air showers. We describe the hadronic interaction models used to
extrapolate results from collider data to ultra-high energies and the main
electromagnetic processes that govern the longitudinal shower evolution. Armed
with these two principal shower ingredients and motivation from the underlying
physics, we describe the different methods proposed to distinguish the primary
particle species. In the end, we explore how ultra-high-energy cosmic rays can
be used as probes of beyond standard model physics models.
