  Models for Type Ia Supernovae (SNe Ia) are reviewed. It is shown that there
are strong reasons to believe that SNe Ia represent thermonuclear disruptions
of C-O white dwarfs, when these white dwarfs reach the Chandrasekhar limit and
ignite carbon at their centers.
  Progenitor scenarios are reviewed critically and the strengths and weaknesses
of each scenario are explicitly presented. It is argued that single-degenerate
models, in which the white dwarf accretes from a subgiant or giant companion
are currently favored. The relation of the different models to the use of SNe
Ia for the determination of cosmological parameters is also discussed.
  Observational tests of the conclusions are suggested.
