  Extensive air showers are complex objects, resulting of billions of particle
reactions initiated by single cosmic ray at ultra-high-energy. Their
characteristics are sensitive both to the mass of the primary cosmic ray and to
the details of hadronic interactions. Many of the interactions that determine
the shower features occur in kinematic regions and at energies beyond those
tested by human-made accelerators. We will report on the measurement of the
proton-air cross section for particle production at a center-of-mass energy per
nucleon of 39 TeV and 56 TeV. We will also show comparisons of post-LHC
hadronic interaction models with shower data by studying the moments of the
distribution of the depth of the electromagnetic maximum, the number and
production depth of muons in air showers, and finally a parameter based on the
rise-time of the surface detector signal, sensitive to the electromagnetic and
muonic component of the shower. While there is good agreement found for
observables based on the electromagnetic shower component, discrepancies are
observed for muon-sensitive quantities.
