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The high luminosity collected by the LHC experiments and the accurate theoretical predictions enable precise tests of the SM under unprecedented conditions. However, severe challenges need to be addressed in order to exploit this untapped potential. The vastness of the LHC data and the variety of possible measurements requires the exploration to be guided towards those quantities or differential distributions that can reveal new physics, compatibly with existing constraints, or that are expected to reveal new physics in concrete BSM scenarios. The possibility of predicting these observables with sufficient accuracy needs to be assessed, and ensured by precision calculations. Finally, experimental strategies need to be devised by which precise measurements are performed of the relevant observables.