  We revisit the stability of the Standard Model vacuum, and investigate its
quantum effective potential using the highest available orders in perturbation
theory and the most accurate determination of input parameters to date. We
observe that the stability of the electroweak vacuum centrally depends on the
values of the top mass and the strong coupling constant. We estimate that
reducing their uncertainties by a factor of two to three is sufficient to
establish or refute SM vacuum stability at the $5\sigma$ level. We further
investigate vacuum stability for a variety of singlet scalar field extensions
with and without flavor using the Higgs portal mechanism. We identify the BSM
parameter spaces for stability and find sizable room for new physics. We
further study the phenomenology of Planck-safe models at colliders, and
determine the impact on the Higgs trilinear, the Higgs-to-electroweak-boson,
and the Higgs quartic couplings, some of which can be significant. The former
two can be probed at the HL-LHC, the latter requires a future collider with
sufficient energy and precision such as the FCC-hh.
