Puzzles, models, and neutrinos in extreme-energy cosmic rays

The observation of twenty cosmic-ray air-showers at and above 10(20) eV poses two problems for particle astrophysics: how the primary particles are accelerated to these energies, and how the primaries get here through the 2.7K microwave background filling the Universe. In addition, the highest-energy events exhibit a surprising small-scale clustering on the celestial sky. 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 role neutrino primaries may play in resolving issues, and (ii) the signatures by which cosmic ray experiments in the near future will discriminate among the proposed models. It is an exciting prospect that highest-energy cosmic rays may have already presented us with new physics not accessible in terrestrial accelerator searches.