Type Ia supernovae are thought to be the outcome of the thermonuclear explosion of a white dwarf in a close binary system. Two possible scenarios, not necessarily incompatible, have been advanced. One assumes a white dwarf that accretes matter from a nondegenerate companion (the single degenerate scenario), the other assumes two white dwarfs that merge as a consequence of the emission of gravitational waves (the double degenerate scenario). The delay time distribution of star formation bursts strongly suggests that the DD scenario should be responsible of the late time explosions, but this contradicts the common wisdom that the outcome of the merging of two white dwarfs is an accretion induced collapse to a neutron star. In this contribution we review some of the most controversial issues of this problem.