  Proposals of measuring the off-shell Higgs contributions and first
measurements at the LHC have electrified the Higgs phenomenology community for
two reasons: Firstly, probing interactions at high invariant masses and
momentum transfers is intrinsically sensitive to new physics beyond the
Standard Model, irrespective of a resonant or non-resonant character of a
particular BSM scenario. Secondly, under specific assumptions a class of models
exists for which the off-shell coupling measurement together with a measurement
of the on-shell signal strength can be re-interpreted in terms of a bound on
the total Higgs boson width. In this paper, we provide a first step towards a
classification of the models for which a total width measurement is viable and
we discuss examples of BSM models for which the off-shell coupling measurement
can be important in either constraining or even discovering new physics in the
upcoming LHC runs. Specifically, we discuss the quantitative impact of the
presence of dimension six operators on the (de)correlation of Higgs on- and
off-shell regions keeping track of all interference effects. We furthermore
investigate off-shell measurements in a wider context of new (non-)resonant
physics in Higgs portal scenarios and the MSSM.
