Type Ia supernovae (SNe Ia) are amongst the most energetic stellar explosions. With typical luminosities several billion times that of the Sun, SNe Ia are visible across a large fraction of the observable universe, and enabled the discovery of its accelerated expansion. These events are thought to result from the thermonuclear disruption of a carbon-oxygen white dwarf (WD) star as it approaches the Chandrasekhar-mass limit, through accretion from a binary companion. However, the nature of this companion and the mechanisms by which the WD explodes are still debated. I will present the numerical setup developed with my collaborators to predict the light curves and spectra of SNe Ia, which provide support to the viability of the standard Chandrasekhar-mass model for most events. However, this standard model is difficult to reconcile with low-luminosity SNe Ia, making a strong case for the existence of multiple progenitor channels for these events.