Type Ia supernovae (SNe Ia) play a crucial role in cosmology as standardizable candles due to empirical correlations between their light curve properties and intrinsic luminosities. These observations are broadly consistent with theoretical models involving the thermonuclear explosion of a carbon-oxygen white dwarf near the Chandrasekhar mass. However, first principles simulations incorporating hydrodynamics, nucleosynthesis, and radiative transfer remain computationally expensive and cannot yet fully reproduce observed features with high precision. This chapter reviews the explosion mechanisms of SNe Ia, focusing on radiative transfer modeling and progenitor system scenarios. The uncertainty in progenitor systems—whether single degenerate or double degenerate—motivates the use of delay time distribution (DTD) modeling and population synthesis to connect observed supernova (SN) rates with theoretical channels. Recent efforts leveraging host galaxy stellar populations and local environments have provided additional constraints on progenitor age and metallicity. Finally, we discuss the growing application of artificial intelligence (AI), particularly convolutional neural networks (CNNs) and physics-informed neural networks (PINNs), in stellar spectroscopy and radiative transfer problems. These AI approaches offer promising pathways to accelerate simulations and solve complex PDEs in a data-driven yet physically consistent manner. Together, these developments represent a multidisciplinary effort to improve our understanding of SNe Ia explosions and their progenitors.