  The long-awaited Higgs particle H around 125 GeV has been observed at the
LHC. Interpreting it as the standard model Higgs boson and if there is no new
physics between electroweak and Planck scale, we then don't have a stable
vacuum. Here, we give a brief review of the electroweak vacuum stability and
some related theoretical issues in the standard model. Possible ways to save
the stability are also discussed.
