The impact of accelerator data on our understanding of extensive air showers

Before the start of CERN in 1954, cosmic rays (CR) were the main source of high energy particles leading to the discovery of anti-matter, muons and first mesons. Then particle accelerators provided controlled environments for studying high-energy particle interactions, producing precise data leading to the development of the Standard Model. These data were used early-on to create models to study extensive air showers (EAS), complex particle cascades initiated by high-energy cosmic rays, but its only in the late 90's that both EAS models and experiments became precise enough to start to see discrepancies between hadronic model predictions and EAS data. Problems like "the muon puzzle", characterized by an unexpected surplus of muons in cosmic ray showers, has propelled further investigations into particle interactions. This talk will discuss how accelerator data have improved the accuracy of EAS models, resolved discrepancies, and offered new insights into hadronic interactions. We will also address the challenges and future directions in integrating accelerator data with EAS observations, underscoring the importance of taking into account all type of colliding system. From the simplest electron-positron annihilation to the most complex Lead-Lead or the newest proton-Oxygen interactions, we need them all to resolve the remaining inconsistencies in the models and finally improve the predictions for Astroparticle physics.