  The Higgs boson, a fundamental scalar, was discovered at CERN in 2012 with
mass 125 GeV, a mass that turned out to be a remarkable choice of Nature. In
the Standard Model of particle physics, the Higgs boson is closely linked to
the mechanism that gives mass to the W and Z gauge bosons that mediate the weak
interactions and to the charged fermions. Following discovery of the Higgs
boson, present measurements at the Large Hadron Collider are focused on testing
the Higgs boson's couplings to other elementary particles, precision
measurements of the Higgs boson's properties and initial investigation of the
Higgs boson's self-interaction and shape of the Higgs potential. With the Higgs
boson mass of 125 GeV the vacuum sits very close to the border of stable and
metastable, which may be a hint to deeper physics beyond the Standard Model.
The Higgs potential also plays an important role in ideas about the
cosmological constant or dark energy that drives the accelerating expansion of
the Universe, the mysterious dark matter that comprises about 80% of the matter
component in the Universe, as well as a possible phase transition in the early
Universe that might be responsible for baryogenesis. Detailed study of the
Higgs boson is at the centre of the recent European Strategy for Particle
Physics update. Here we review the present status of this physics and discuss
the new insights expected from present and future experiments.
