Because calibrated light curves of type Ia supernovae have become a
major tool to determine the local expansion rate of the Universe and
its geometrical structure, considerable attention has been given to
models of these events over the past couple of years. Here we address
recent progress in modelling them by means of 3-dimensional
hydrodynamic simulations. The 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 modelled by means of numerical methods which have
been developed and tested for laboratory and technical flames. It is
shown that the 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. 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 discussed.