In this article the stability of the Standard Model (SM) vacuum
in the presence of radiative corrections and for a Higgs boson with a mass in the vicinity of $125$ GeV is discussed.
The central piece in this discussion will be the Higgs self-interaction $\lambda$ and
its evolution with the energy scale of a given physical process.
This is described by the $\beta$-function to which we recently computed analytically the
dominant three-loop contributions.
These are mainly the QCD and top-Yukawa corrections as well as
the contributions from the Higgs self-interaction itself. We will see that
for a Higgs boson with a mass of about $125$ GeV the question whether the SM vacuum is stable
and therefore whether the SM could be
valid up to Planck scale cannot be answered with certainty due to large
experimental uncertainties, mainly in the top quark mass.