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I review the state-of-the-art concerning the treatment of high energy cosmic ray interactions in the atmosphere, discussing in some detail the underlying physical concepts and the possibilities to constrain the latter by current and future measurements at the Large Hadron Collider. The relation of basic characteristics of hadronic interactions tothe properties of nuclear-electromagnetic cascades induced by primary cosmic rays in the atmosphere is addressed.
Predictions of popular cosmic ray interaction models for some basic characteristics of cosmic ray-induced extensive air showers are analyzed in view of experimental data on proton-proton collisions, obtained at the Large Hadron Collider. The differences between the results are traced down to different approaches for the treatment of hadronic interactions, implemented in those models. Potential measurements by LHC and cosmic ray experiments, which could be able to discriminate between the alternative approaches, are proposed.