Recent progress in modeling type Ia supernovae by means of 3-dimensional
hydrodynamic simulations as well as several of the still open questions are
addressed. Our models are based on the assumption that thermonuclear burning
inside a Chandrasekhar-mass C+O white dwarf is similar to turbulent chemical
combustion and that, thus, thermonuclear supernovae can be modeled by means
of numerical methods which have been developed and tested for laboratory and
technical flames. It is shown that the new models have considerable
predictive power and allow to study observable properties of type Ia
supernovae, such as their light curves and spectra, without adjustable
non-physical parameters, and they make firm predictions for the
nucleosynthesis yields from the explosions. This raises a quest for better
data, covering the spectroscopical and photometric evolution in all wave
bands from very early epochs all the way into the nebular phase. First such
results obtained by the European Supernova Collaboration (ESC) for a sample
of nearby SNe Ia and their implications for constraining the models and
systematic differences between them are also discussed.