  Contrary to earlier expectations, several cosmic ray events with energies
above $10^{20}$ eV have been reported by a number of ultra-high energy cosmic
ray observatories. According to the AGASA experiment, the flux of such events
is well above the predicted Greisen-Zatsepin-Kuzmin cutoff due to the pion
production 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 small scale clustering
strongly challenge all models proposed to resolve this puzzle. We discuss how
the GZK cutoff is modified by the local distribution of galaxies and how
astrophysical proton sources with soft injection spectra are ruled out by AGASA
data. Sources with hard injection spectrum are barely allowed by the observed
spectrum. If the most recent claims by AGASA that the highest energy events are
due to clustered nuclei are confirmed, the most plausible explanation are
astrophysical sources with very hard spectra such as extragalactic unipolar
inductors. In addition, extragalactic magnetic fields need to be well below the
current nano-Gauss upper limits. Alternatively, if the primaries are not
nuclei, the need for new physics explanations is paramount. We present an
overview of the theoretical proposals along with their most general signatures
to be tested by upcoming experiments.
