Constraining Extended Scalar Sectors at the LHC and beyond

We give a brief overview of beyond the Standard Model (BSM) theories with an extended scalar sector and their phenomenological status in the light of recent experimental results. We discuss the relevant theoretical and experimental constraints, and show their impact on the allowed parameter space of two specific models: the real scalar singlet extension of the Standard Model (SM) and the Inert Doublet Model. We emphasize the importance of the LHC measurements, both the direct searches for additional scalar bosons, as well as the precise measurements of properties of the Higgs boson of mass 125 GeV. We show the complementarity of these measurements to electroweak and dark matter observables.
Comment: 18 pages, 8 figures; prepared for submission to MPLA (invited review) v2: several references and small text modification added to align with journal version. 2 small errors in plots corrected