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.