  From the spectra and light curves it is clear that SNIa 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 (LC), 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. The general methods and critical
tests are presented (sect. 2).
  Different models for the thermonuclear explosion are discussed including
detonations, deflagrations, delayed detonations, pulsating delayed detonations
(PDD) and helium detonations (sect.3). Comparisons between theoretical and
observed LCs and spectra provide an insight into details of the explosion and
nature of the progenitor stars (sect. 4/5). We try to answer several related
questions. Are subluminous SNe Ia a group different from `normal' SN Ia (sect.
5)? Can we understand observed properties of the LCs and spectra (sect. 4)?
What do we learn about the progenitor evolution and its metallicity (sect. 3,
Figs. 4,5)? Do successful SN~Ia models depend on the type of the host galaxy
(Table 2)? Using both the spectral and LC information, theoretical models allow
for a determination of the Hubble constant independent from `local' distance
indicators such as delta-Cephei stars. Ho is found to be 67 +- 9km/s/Mpc and,
from SN1988U, qo equals 0.7 +- 1. within 95 percent confidence levels.
