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The discovery of the Higgs boson by the LHC and the measurement of its massat around 125 GeV, taken together with the absence of signals of physics beyondthe standard model, make it possible that we might live in a metastableelectroweak vacuum. Intriguingly, we seem to be very close to the boundary ofstability and this near-criticality makes our vacuum extremely long-lived. Inthis talk I describe the state-of-the-art calculation leading to these results,explaining what are the ingredients and assumptions that enter in it, withspecial emphasis on the role of the top mass. I also discuss possibleimplications of this metastability for physics beyond the standard model andcomment on the possible impact of physics at the Planck scale onnear-criticality.

Implications of the top (and Higgs) mass for vacuum stability