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Hadronic models for strong interactions in a regime of low momentum exchange (often referred to as soft QCD) are of crucial importance for modelling the primary interaction of a cosmic ray particle with an atmospheric nucleus as well as backgrounds from multiple simultaneous hadronic interactions in collisions at the Large Hadron Collider. In this talk, several LHC experiments and physics analyses are presented which could improve the modelling of soft QCD processes with the currently available event generators.