  Contrary to expectations, several cosmic ray events with energies above
$10^{20}$ eV have been observed. The flux of such events is well above the
predicted Greisen-Zatsepin-Kuzmin cutoff due to the pion production (via the
$\Delta$ resonace) of extragalactic cosmic ray protons off the cosmic microwave
background. In addition to the relatively high flux of events, the isotropic
distribution of arrival directions and an indication of hadronic primaries
strongly challenge all models proposed to resolve this puzzle. Models based on
astrophysical accelerators need to invoke strong Galactic and extragalactic
magnetic fields with specific properties which are yet to be observed, while
models based on physics beyond the standard model of particle physics generally
predict photon primaries contrary to experimental indications. The resolution
of this puzzle awaits a significant increase in the data at these energies
which will be provided by future experiments.
