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

The observation of twenty cosmic-ray air-showers at and above 10(20) eV pos es two problems for particle astrophysics: how the primary particles are ac celerated to these energies, and how the primaries get here through the 2.7 K microwave background filling the Universe. In addition, the highest-energ y 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 s ignatures by which cosmic ray experiments in the near future will discrimin ate among the proposed models. It is an exciting prospect that highest-ener gy cosmic rays may have already presented us with new physics not accessibl e in terrestrial accelerator searches.