  The study of the Higgs boson properties offers compelling perspectives for
testing the effects of physics beyond the Standard Model and has deep
implications for the LHC program and future colliders. Accurate determinations
of the Higgs boson properties can provide us with a distinctively precise
picture of the Higgs sector, set tight bounds, and predict ranges for the
values of new physics model parameters. In this paper, we discuss the
constraints on supersymmetry that can be derived by a determination of the
Higgs boson mass and couplings. We quantify these constraints by using scans of
the 19-parameter space of the so-called phenomenological minimal supersymmetric
Standard Model. The fraction of scan points that can be excluded by the Higgs
measurements is studied for the coupling measurement accuracies obtained in LHC
Run 2 and expected for the HL-LHC program and $e^+e^-$ colliders and contrasted
with those derived from missing transverse energy searches at the LHC and from
dark matter experiments.
