Two types of supernovae are considered: thermonuclear supernovae, whose explosions are due to thermonuclear energy, and core-collapse supernovae, whose explosions are due to the gravitational energy of collapsing stars released in the form of neutrinos. Numerical models of supernovae are discussed. The main problem in devising supernova explosion mechanisms is producing the energy required to disperse the envelope. In theoretical models, it is necessary to solve multi-dimensional problems involving complex physics (3D gas dynamics, neutrino transport, large-scale convective instability, and other important physical processes). In recent years, the development of large-scale convection during supernova explosions has been reconsidered. Self-consistent problems problems in three-dimensional, gas-dynamical instability have been considered. Two-dimensional gas-dynamical calculations taking into account neutrino absorption in the envelope have been performed. The spherically symmetric collapse and neutrino transport were calculated including all reactions, leading to a new understanding of possible paths for the development of supernova theory. The main emphasis is placed on the neutrino transport and the basis for promising multidimensional models taking into account large-scale convective instability.