One Higgs was found. Are there more? In this work we discuss simple extension of the scalar sec-
tor of the Standard Model (SM) used as benchmark models by ATLAS and CMS in the searches for new scalars at the LHC. We discuss how much the discovered 125 GeV Higgs at the LHC resembles the SM Higgs and how will our understanding of the Higgs nature improve at future electron-positron colliders. Models with extended Higgs sectors provide very interesting scenarios, from the existence of charged Higgs bosons to CP-violating scalars that can be probed by the
experimental collaborations at the LHC. Comparison between the rates in the different models show that in some cases the models could be distinguished.