While Type Ia supernovae are widely used as distance indicators, the reasons for the correlation between luminosity and light curve width that allows SNe Ia to be calibratable standard candles is not yet fully understood, and in particular the details of the explosion mechanism are still the subject of heated debate. We present the results of a systematic approach that uses the high-quality data collected by the European Research Training Network “The Physics of Type Ia Supernova Explosions” to map the supernova ejecta and to infer the properties of the explosion.