Since more than 40 years several formal results hinted for additional effects beyond perturbation theory even at weak coupling in theories with a Brout-Englert-Higgs effects. In this talk analytical and lattice results are presented for processes, like vector boson scattering and lepton colliders, demonstrating that these effects are present and possibly detectable in experiments. Furthermore, in many BSM scenarios the same effects yield qualitative, rather than quantitative consequences, as will be briefly surveyed.