New physics is expected to exist because of several observational shortcomings of the Standard Model. The scale at which the Standard Model needs to be completed is however not known. Great hopes for finding new physics at collider accessible energies are motivated by theoretical puzzles such as the lightness of the Higgs boson, but still there is room for one or more orders of magnitude of uncertainty as to how large the new physics scale ought to be. In my talk I will present new ways in which the LHC can probe new physics from the 100 GeV to 10 TeV scale making very precise and well aimed measurement of certain observables. This is a search strategy in which lepton colliders such as LEP are usually the only viable ones. Thanks to recent progress in SM calculations, hadron colliders such as LHC have now a chance to pursue meaningful searches along this strategy as well. I will discuss how few percent precision "low-energy" and ten percent precision "high-enegrgy" measurements of top quark and electroweak boson productions can potentially highlight the first signs of physics beyond the Standard Model.