An introductory overview of the reasons for interest in the highest-energy cosmic rays including the challenge of acceleration will be given. Measurements of the energy spectrum, arrival direction distribution and mass composition of the cosmic rays above 10^18 eV, made recently at the Pierre Auger Observatory, will be discussed in some detail. The flux of cosmic rays is found to be strongly suppressed above 4x10^19 eV and above a similar energy the distribution of the arrival directions of the particles indicates an anisotropy of 40%. These two conclusions are nearly independent of assumtions about particle physics parameters. However while the anisotropy is indicative of a substantial fraction of protons in the primary cosmic ray beam, measurements of the mass composition suggest that the fraction of heavier nuclei grows as the energy increases.This interpretation, however, depends on extrapolations of cross-sections, multiplicity and inelasticity to centre-of-mass energies well beyond what will be reached at the LHC. It is not clear how these conflicting results can be reconciled: some suggestions will be offered.