The interpretation of LHC data, and the assessment of possible hints for new physics in the experimental signals, require the precise knowledge of the proton subnuclear structure in terms of its elementary constituents, quarks and gluons. In this talk I will present the fascinating precision frontier that phenomenologists are facing an will describe the challenges behind the determination of proton structure, involving precise perturbative QCD calculations and machine learning techniques. I will show how global fits of the proton might inadvertently ‘fit away’ signals of new physics in the high-energy tails of the distributions that are experimentally measured. A new physics scenario in which the fit of the proton’s structure may completely absorb such signs of new physics is showcased. Strategies to single out such effects and disentangle the inconsistencies that stem from new physics signals are discussed.