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