  From the spectra and light curves it is clear that SNIa events are
thermonuclear explosions of white dwarfs. However, details of the explosion are
highly under debate. Here, we present detailed models which are consistent with
respect to the explosion mechanism, the optical and infrared light curves, and
the spectral evolution. This leaves the description of the burning front and
the structure of the white dwarf as the only free parameters. The explosions
are calculated using one-dimensional Lagrangian codes including nuclear
networks. Subsequently, optical and IR-LCs are constructed. Detailed
NLTE-spectra are computed for several instants of time using the density,
chemical and luminosity structure resulting from the LCs.
  Different models for the thermonuclear explosion are discussed including
detonations, deflagrations, delayed detonations, pulsating delayed detonations
(PDD) and helium detonations. Comparisons between theoretical and observed LCs
and spectra provide an insight into details of the explosion and nature of the
progenitor stars. We try to answer several related questions. Are subluminous
SNe Ia a group different from `normal' SN Ia? Can we understand observed
properties of the LCs and spectra?What can we learn from infrared spectra? Can
we determine $H_o$ independently from primary distance indicators, and how do
the results compare with empirical methods? What do we learn about the
progenitor evolution and its metallicity? What are the systematic effects for
the determination of the cosmological parameters $\Omega_M$ and $\Lambda$ and
how can we recognize this potential 'pitfalls' and correct for evolutionary
effects?
