Matching relations for decoupling in the standard model at two loops and beyond

I discuss the matching relations for the running renormalizable parameters when the heavy particles (top quark, Higgs scalar, Z and W vector bosons) are simultaneously decoupled from the standard model. The complete two-loop-order matching for the electromagnetic coupling and all light fermion masses is obtained, augmenting existing results at four-loop order in pure QCD and in complete two-loop order for the strong coupling. I also review the further sequential decouplings of the lighter fermions (bottom quark, tau lepton, and charm quark) from the low-energy effective theory.