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Depending on its initial mass, a star may end as a white dwarf or explode as a supernova. The dividing boundary is however ill-defined, and depends on the treatment of convection and mass loss. Asymptotic Giant Branch (AGB) stars do not ignite carbon and end up as carbon-oxygen white dwarfs. But if mass loss is weak the core may grow to reach the Chandrasekhar mass limit and explode as a thermonuclear supernova. Slightly more massive stars ignite carbon and, like AGB stars, they also undergo thermal pulses. These super-AGB stars may leave an oxygen-neon white dwarf, but their fate is unclear. They will either produce an oxygen-neon white dwarf or explode in an electron capture supernova and produce a neutron star. Red supergiants of initial mass as low as 8 solar masses have now been identified directly as the progenitors of type IIP supernovae. With the Initial Mass Function favouring the low mass end of the supernova progenitors, massive AGB stars contributing to nitrogen enrichment on timescales as short as tens of million years, and both supernovae and AGB stars competing for the title of most prolific dust factory in the early Universe, it is crucial to gain a better understanding of the boundary between massive AGB stars and the progenitors of core-collapse supernovae.