Extensive air showers are the result of billions of particle reactions initiated by single cosmic rays at ultra-high energy. Their characteristics are sensitive both to the mass of the primary cosmic ray and to the fine details of hadronic interactions. Ultra-high energy cosmic rays can be used to experimentally extend our knowledge on hadronic interactions in energy and kinematic regions beyond those tested by human-made accelerators. We report on how the Pierre Auger Observatory is able to measure the proton-air cross section for particle production at a center-of-mass energy per nucleon of 39 TeV and 56 TeV and also to constrain the new hadronic interaction models tuned after the results of the Large Hadron Collider, by measuring: the average shape of the electromagnetic longitudinal profile of air showers, the moments of the distribution of the depth at which they reach their maximum, and the content and production depth of muons in air showers with a primary center-of-mass energy per nucleon around and above the 100 TeV scale.