Spectroscopic and photometric evidence indicates that Type la supernovae (SNe Ia) are the thermonuclear explosions of accreting white dwarfs. However, the progenitor binary systems and hydrodynamical models for SNe Ia are still controversial, The relatively uniform light curves and spectral evolution of SNe Ia have led to their use as a standard candle for determining cosmological parameters, such as the Hubble constant, the density parameter, and the cosmological constant, Recent progress includes the calibration of the absolute maximum brightness of SNe Ia with the Hubble Space Telescope, the reduction of the dispersion in the Hubble diagram through the use of the relation between the light curve shape and the maximum brightness of SNe Ia, and the discovery of many SNe Ia with high red shifts.