  We give a brief review of beyond-the-Standard Model (BSM) extensions of the
Standard Model (SM) Higgs sector. Going from very simple to more complicated
models, our survey includes models with additional scalar singlet fields, the
Two Higgs Doublet Model (2HDM) and the Higgs sector of the Minimal
Supersymmetric Standard Model (MSSM). We discuss the impact of current
experimental results from LHC Higgs searches and measurements and the
prospective reach of the LHC in the high-luminosity (HL) phase. We furthermore
highlight possible new collider signatures within these models that have not
been experimentally probed to date.
