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The flux suppression at the highest energies

Almost half a century ago, Greisen, Zatsepin and Kuz'min (GZK) predicted a "cosmologically meaningful termination" of the spectrum of cosmic rays at energies around $10^{20}$ eV due to their interaction with the cosmic microwave background, as they propagate from distant extragalactic sources. A suppression of the flux above $4\times 10^{19}$ eV is now confirmed. We argue that current data are insufficient to conclude whether the observed feature is due to energy loss during propagation, or else to the fact that the astrophysical accelerators reach their limit, or indeed to a combination of both source properties and propagation effects. We discuss the dependence of the spectral steepening upon the cosmic-ray composition, source properties, and intervening magnetic fields, and speculate on the additional information that may be necessary to reach unambiguous conclusions about the origin of the flux suppression and of the mechanisms behind the acceleration of cosmic rays up to the highest observed energies.