Invited review talk at conference on the AGB-Supernovae mass transition

On March 27-31 an international astrophysics conference on the AGB-Supernovae mass transition was held at the Observatory of Rome in Frascati, Italy. About 100 researchers from all over the world discussed the evolution of stars that start their life with a mass of about 7 to 11 solar masses and reach the super-asymptotic giant branch (AGB) phase during their later evolution. At least three different types of supernovae are connected with the limits of this mass range: isolated stars with an initial mass larger than 11 solar masses end their lives as core collapse supernovae (Type II SN). An initial stellar mass of 7 solar masses is the upper limit for the formation of carbon-oxygen white dwarf stars, whose subsequent evolution through mass transfer in a binary system may lead to thermonuclear supernova explosions (Type Ia SN). Finally, single stars in the super-AGB upper mass range may be the site of electron-capture supernovae. I was invited to provide a review about recent progress in the modelling of Type Ia supernovae on this conference.