The observation of twenty cosmic-ray air-showers at and above 10^{20} eV
poses fascinating problems for particle astrophysics: how the primary particles
are accelerated to these energies, how the primaries get here through the 2.7K
microwave background filling the Universe, and how the highest-energy events
exhibit clustering on few-degree angular scales on the sky when charged
particles are expected be bent by cosmic magnetic fields. An overview of the
puzzles is presented, followed by a brief discussion of many of the models
proposed to solve these puzzles. Emphasis is placed on (i) the signatures by
which cosmic ray experiments in the near future will discriminate among the
many proposed models, and (ii) the role neutrino primaries may play in
resolving the observational issues. It is an exciting prospect that
highest-energy cosmic rays may have already presented us with new physics not
accessible in terrestrial accelerator searches.Comment: 12 pages, RevTeX, 4 figures, Expansion of talks given at NU2000
(Canada); Metepec, Mexico; RADHEP2000 (UCLA
