The Pierre Auger Observatory was designed to study the properties of cosmic rays with energies above 10^18 eV to beyond 10^20 eV and with it results of importance for astrophysics and particle physics have been obtained. The astrophysical interest lies in discovering the sources of these particles and for this one needs to measure the energy spectrum and the mass composition: the measurements rely, to a lesser and greater extent respectively, on knowledge of hadronic physics, such as cross-section, multiplicity and inelasticity, at centre-of-mass energies up to ~30 times above what is accessible at the LHC. After describing the Auger Observatory, I will discuss our calorimetric measurement of the primary energy which can be made with an accuracy of ~ 10%, independent of the unknown hadronic physics, and the astrophysical implications of the result which also require knowledge of the primary mass. I will mention – very briefly – two new results on the anisotropy of the highest-energy particles.
Efforts to determine the primary mass are challenged by our lack of knowledge of the hadronic physics at energies beyond the LHC, but consistent features about the variation of the mass with energy are emerging – although dramatic changes in hadronic features at extreme energies, such as a huge rise the p-air cross-section, cannot be excluded. To help clarify the situation, a measurement of the p-air cross-section at sqrt(S) ~ 57 TeV has been made which is found to agree well with extrapolations from machine energies. However discrepancies are found between what is predicted and what is observed in the muon properties of showers. Similar anomalies may have been seen in the multi-muon observations at the LEP experiments and in ALICE. These results call for further refinement of the extrapolations from LHC energies and may therefore lead to new insights about hadronic interactions at the highest energies.