Type Ia supernovae, widely believed to result from thermonuclear explosions of white dwarfs, are extremely important phenomena in the Universe, owing to their roles as distance indicators in cosmology. However, many of their fundamental aspects, e.g., how their progenitors evolve and explode, remain elusive. I will present recent progress in observational and theoretical studies toward solving this issue, and also discuss future prospects mainly for high-resolution X-ray spectroscopy of Type Ia supernova remnants with XRISM and Athena.