The extensive surface convection zone of a red giant star becomes deeper and deeper, as the star evolves. In some cases it reaches the bottom of the hydrogen-rich envelope and even penetrates into the stellar core. From the standpoint of entropy distribution in the star, the structure of the convective envelope and the mechanism of its penetration into the core are summarized. Possibilities of the penetration are discussed for stars of masses in the range of 1–60 M⊙ over their entire lifetimes of evolution. Effects of uncertainty in the mixing length theory of convection, neutrino loss and thermal instability of helium-burning shell are studied also. When the convection penetrates into the core, material of the core is brought up to the stellar surface and the star will be a peculiar star. It is concluded that there are possibilities to interpret the origin of peculiar stars with luminosities fainter than 7 × 104L⊙, but that the more luminous ones do not originate from the penetration of surface convection.

A survey is given of the present state of theories concerned with the mechanism of supernova outbursts. Special attention is paid to the state of the star immediately before the supernova explosion (presupernova).

The following topics are discussed.

(1) The thermonuclear model of supernova explosions.

(2) The gravitational collapse model of supernova explosions.

(3) The characteristics of presupernova models resulting from the comparison of theoretical light curves with observational ones.