  We summarize recent work on the consistent calculation of bubble-nucleation
rates. Our approach is based on the notion of a real coarse-grained potential.
The bubble-nucleation rate is calculated through an expansion around the
semiclassical saddle point associated with tunnelling. We resolve outstanding
problems related to the convexity of the potential, the double-counting of the
effect of fluctuations and the inherent ultraviolet divergences. We determine
the region of validity of the expansion around the saddle point. We find that
this expansion fails near the spinodal line, and for weak or
radiatively-induced first-order phase transitions. We apply our method to the
bound on the Higgs-boson mass from vacuum metastability and the electroweak
phase transition.
