False vacuum decay is the first-order phase transition of fundamental fields. Vacuum instability plays a very important role in particle physics and cosmology. Theoretically, any consistent theory beyond the Standard Model must have the lifetime of the electroweak vacuum longer than the age of the Universe. Phenomenologically, first-order cosmological phase transitions can be relevant for baryogenesis and gravitational wave production. In this talk, I will introduce some recent theoretical developments on false vacuum decay, including radiative corrections on false vacuum decay, real-time formalism and a possible correspondence between thermal and quantum vacuum transitions around horizons.