Implications of the Higgs boson discovery

With the discovery of the Higgs boson by the LHC in 2012, a new era started in which we have direct experimental information on the physics behind the breaking of the electroweak (EW) symmetry. This breaking plays a fundamental role in our understanding of particle physics and sits at the high-energy frontier beyond which we expect new physics that supersedes the Standard Model (SM). In this review we summarize what we have learned so far from LHC data in this respect. In the absence of new particles having been discovered, we discuss how the scrutiny of the properties of the Higgs boson (in search for deviations from SM expectations) is crucial as it can point the way for physics beyond the SM. We also emphasize how the value of the Higgs mass could have far-reaching implications for the stability of the EW vacuum if there is no new physics up to extremely large energies.