  Whether the Standard Model electroweak vacuum is stable, metastable or
unstable depends crucially on the top mass (and, to a lesser extent, on other
measurable quantities). These topics are reviewed and updated by taking into
account the most recent determination of the top and Higgs masses. Moreover,
the correction to the vacuum decay due to Einstein gravity is described. This
process is also discussed in a scenario, called softened gravity, which has
been proposed as a solution of the Higgs mass hierarchy problem.
