Vacuum Stability in the Standard Model

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.