| Summary: | The Large Hadron Collider forward (LHCf) experiment studies the production of neutral particles in the very forward region of high-energy hadronic collisions at the LHC. These measurements provide essential calibration data for hadronic interaction models used in simulations of extensive air showers initiated by ultra-high-energy cosmic rays. The LHCf experiment measures forward-produced neutral particles, such as neutrons, photons, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>π</mi><mn>0</mn></msup></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula> mesons, which play a key role in the development of extensive air showers. Proton–proton collisions at the LHC reach center-of-mass energies up to 13.6 TeV, corresponding in the fixed-target frame to cosmic-ray interactions at energies close to 10<sup>17</sup> eV in the Earth’s atmosphere. LHCf has collected data in proton–proton collisions at several energies, as well as in proton–lead collisions, enabling detailed comparisons between experimental results and predictions of hadronic interaction models. This contribution reviews the most significant LHCf results, with emphasis on Run II proton–proton data at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mi>TeV</mi></mrow></semantics></math></inline-formula>, including measurements of forward neutron, photon, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula> meson production. Finally, future prospects are discussed, focusing on ongoing analyses of Run III proton–proton data at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13.6</mn><mi>TeV</mi></mrow></semantics></math></inline-formula> and on the final LHCf operation in proton-oxygen collisions at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>9.6</mn><mi>TeV</mi></mrow></semantics></math></inline-formula>, which best reproduces cosmic-ray interactions with nuclei of the Earth’s atmosphere.
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