  The origin of cosmic rays with energies higher than 10$^{20}$ eV remains a
mystery. Accelerating particles up to these energies is a challenge even for
the most energetic astrophysical objects known. While the isotropy in arrival
directions argues for an extra-galactic origin, the photon-pion production off
the cosmic background radiation limits the sources of such particles to systems
less than 50 Mpc away from us. The combination of large gyroradii, efficient
energy losses, and isotropic arrival directions defies most of the proposed
astrophysical accelerators as well as the more exotic alternatives. I briefly
review theoretical models for the acceleration and propagation of
ultra-high-energy cosmic-rays and discuss the potential for future
observatories to resolve this cosmic mystery.
