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Type Ia supernovae are used as distance indicators to measure the expansion rate of the Universe and to constrain the nature of dark energy. Current and upcoming surveys will allow to extend supernova Hubble diagrams to higher redshifts and to improve further their statistics.  It is accepted that Type Ia supernovae are thermonuclear explosions of carbon-oxygen white dwarfs in binary systems. However, the identification of their progenitors, the evolutionary path leading to the explosion and the explosion mechanism itself have not been identified yet. This is critical, as we need to understand the potential evolution of their luminosity with cosmic time and, thus, with their stellar progenitors.  We will review the current situation, considering observational hints. We will focus on our recent models, that follow the evolution of carbon-oxygen white dwarfs accreting mass up to thermonuclear runaway, and on their dependence with the initial metallicity of the white dwarf progenitors.

Type Ia SN progenitors: pre-explosion phase in nearly Chandrasekhar mass WDs