Vacuum Stability and the Higgs Boson

The discovery of the Higgs boson at the LHC, and especially the determination of its mass around 125 GeV, together with the absence of any trace of new physics make it conceivable that we live in a metastable (but long-lived) electroweak vacuum. I will describe the state-of-the-art calculation that leads to this conclusion, elaborate on possible implications as well as cures of this instability of the Higgs potential and discuss some possible lines of attack for lattice studies of such metastability.