  In 1981 Icko Iben Jr published a paper entitled 'The carbon star mystery: why
do the low mass ones become such, and where have all the high mass ones gone?',
where he discussed the discrepancy between the theoretical expectation and its
observational counterpart about the luminosity function of AGB carbon stars.
After more than 40 years, our understanding of this longstanding problem is
greatly improved, also thanks to more refined stellar models and a growing
amount of observational constraints. In this paper we review the state of the
art of these studies and we briefly illustrate the future perspectives.
