Type Ia supernovae are dramatic explosions that can outshine a whole galaxy for a short period of time. In the past two decades, they have been used as standardisable candles to measure the expansion history of the Universe. There is a wide consensus that Type Ia supernovae originate from thermonuclear explosions of carbon-oxygen white dwarfs in binary systems. However, the actual progenitor stars are still elusive and details of the explosion mechanism are not yet fully understood. In this talk, I will present how a synthesis of numerical explosion models and observational data can be used to shed light on these questions.