  Although cosmic rays were discovered 90 years ago, we do not know how and
where they are accelerated. There is compelling evidence that the highest
energy cosmic rays are extra-galactic -- they cannot be contained by our
galaxy's magnetic field anyway because their gyroradius exceeds its dimensions.
Elementary elementary-particle physics dictates a universal upper limit on
their energy of $5\times10^{19}$ eV, the so-called Greisen-Kuzmin-Zatsepin
cutoff; however, particles in excess of this energy have been observed, adding
one more puzzle to the cosmic ray mystery. Mystery is nonetheless fertile
ground for progress: we will review the facts and mention some very speculative
interpretations. There is indeed a realistic hope that the oldest problem in
astronomy will be resolved soon by ambitious experimentation: air shower arrays
of $10^4$ km$^2$ area, arrays of air Cerenkov detectors and kilometer-scale
neutrino observatories.
