  We review the physics of the highest energy cosmic rays. The discovery of
their sources, still unknown, will reveal the most energetic astrophysical
objects in the universe and could unveil new physics beyond the standard model
of particle physics. We discuss the details of propagation of these high energy
particles, their interaction with astrophysical photon backgrounds and
intergalactic magnetic fields, and the production of secondary cosmogenic
particles associated to their transport. We examine different models of
acceleration, reviewing the principal astrophysical objects that could energise
cosmic rays until the highest energies. Given the uncertainties in the observed
mass composition, we review the two alternative scenarios of a composition made
only by protons or by protons and heavier nuclei; discussing the consequences
of the two scenarios in terms of sources, acceleration mechanisms and
production of secondary cosmogenic gamma rays and neutrinos.
