  Models for Type Ia Supernovae (SNe Ia) are reviewed. It is shown that there
are strong reasons to believe that most SNe Ia represent thermonuclear
disruptions of C-O white dwarfs, when these white dwarfs reach the
Chandrasekhar limit and ignite carbon at their centers.
  Different progenitor scenarios are reviewed critically and the strengths and
weaknesses of each scenario are presented in detail. It is argued that
theoretical considerations currently favor single-degenerate models, in which
the white dwarf accretes from a subgiant or giant companion. However, it is
still possible that more than one progenitor class contributes to the observed
sample. The relation of the different models to the use of SNe Ia for the
determination of cosmological parameters is discussed. It is shown that while
the observed diversity of SNe Ia may argue for the existence of different
progenitor classes, this does not affect the interpretation of an accelerating
expansion of the universe.
