  The primary ultrahigh energy particles which produce giant extensive air
showers in the Earth's atmosphere present an intriguing mystery from two points
of view: (1) How are these particles produced with such astounding energies,
eight orders of magnitude higher than those produced by the best man-made
terrestrial accelerators? (2) Since they are most likely extragalactic in
origin, how do they reach us from extragalactic distances without suffering the
severe losses expected from interactions with the 2.7 K thermal cosmic
background photons -- the so-called GZK effect? The answers to these questions
may involve new physics: violations of special relativity, grand unification
theories, and quantum gravity theories involving large extra dimensions. They
may involve new astrophysical sources, "zevatrons". Or some heretofore totally
unknown physics or astrophysics may hold the answer. I will discuss here the
mysteries involving the production and extragalactic propagation of ultrahigh
energy cosmic rays and some suggested possible solutions.
