  The major role type Ia supernovae play in many fields of astrophysics and in
particular in cosmological distance determinations calls for self-consistent
models of these events. Since their mechanism is believed to crucially depend
on phenomena that are inherently three-dimensional, self-consistent numerical
models of type Ia supernovae must be multi-dimensional. This field has recently
seen a rapid development, which is reviewed in this article. The different
modeling approaches are discussed and as an illustration a particular explosion
model -- the deflagration model -- in a specific numerical implementation is
presented in greater detail. On this exemplary case, the procedure of
validating the model on the basis of comparison with observations is discussed
as well as its application to study questions arising from type Ia supernova
cosmology.
