Towards an understanding of Type Ia supernovae from a synthesis of
  theory and observations
  Motivated by the fact that calibrated light curves of Type Ia supernovae (SNe
Ia) have become a major tool to determine the expansion history of the
Universe, considerable attention has been given to, both, observations and
models of these events over the past 15 years. Here, we summarize new
observational constraints, address recent progress in modeling Type Ia
supernovae by means of three-dimensional hydrodynamic simulations, and discuss
several of the still open questions. It will be be shown that the new models
have considerable predictive power which allows us to study observable
properties such as light curves and spectra without adjustable non-physical
parameters. This is a necessary requisite to improve our understanding of the
explosion mechanism and to settle the question of the applicability of SNe Ia
as distance indicators for cosmology. We explore the capabilities of the models
by comparing them with observations and we show how such models can be applied
to study the origin of the diversity of SNe Ia.
