We review some of the recent progress in our knowledge about high-energy cosmic rays, with an emphasis on the interpretation of the different observational results. We discuss the effects that are relevant to shape the cosmic ray spectrum and the explanations proposed to account for its features and for the observed changes in composition. The physics of air-showers is summarized and we also present the results obtained on the proton-air cross section and on the muon content of the showers. We discuss the cosmic ray propagation through magnetic fields, the effects of diffusion and of magnetic lensing, the cosmic ray interactions with background radiation fields and the production of secondary neutrinos and photons. We also consider the cosmic ray anisotropies, both at large and small angular scales, presenting the results obtained from the TeV up to the highest energies and discuss the models proposed to explain their origin.
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