This review by Wolfgang Hillebrandt and Jens C. Niemeyer discusses the models of Type Ia supernovae, which have become crucial for determining the local expansion rate of the universe and its geometrical structure. Type Ia supernovae are believed to result from the thermonuclear explosions of white dwarfs that have approached the Chandrasekhar mass, typically around 1.39 solar masses. The review addresses recent progress in modeling these events, including the explosion mechanism and related physical processes, such as turbulent nuclear combustion in degenerate stars. It also discusses observational constraints and the diversity among Type Ia supernovae, highlighting the need for a robust explosion model that can account for the observed homogeneity and variability. The authors review numerical techniques for modeling light curves and spectra, noting the challenges in accurately calculating opacities and radiation transport. They conclude by discussing the progenitor systems of Type Ia supernovae, favoring Chandrasekhar-mass C+O white dwarfs as the primary candidates, though acknowledging the possibility of other progenitors, such as sub-Chandrasekhar models or accretion-induced collapse of massive white dwarfs.This review by Wolfgang Hillebrandt and Jens C. Niemeyer discusses the models of Type Ia supernovae, which have become crucial for determining the local expansion rate of the universe and its geometrical structure. Type Ia supernovae are believed to result from the thermonuclear explosions of white dwarfs that have approached the Chandrasekhar mass, typically around 1.39 solar masses. The review addresses recent progress in modeling these events, including the explosion mechanism and related physical processes, such as turbulent nuclear combustion in degenerate stars. It also discusses observational constraints and the diversity among Type Ia supernovae, highlighting the need for a robust explosion model that can account for the observed homogeneity and variability. The authors review numerical techniques for modeling light curves and spectra, noting the challenges in accurately calculating opacities and radiation transport. They conclude by discussing the progenitor systems of Type Ia supernovae, favoring Chandrasekhar-mass C+O white dwarfs as the primary candidates, though acknowledging the possibility of other progenitors, such as sub-Chandrasekhar models or accretion-induced collapse of massive white dwarfs.