The determination of the Mass Function (MF) at the bottom of the Main Sequence is subject to severe uncertainties, due both to the very low intrinsic luminosity of these stars and to their rapidly varying Mass-Luminosity (ML) relation. A potentially very important field of exploration, although its present results are still to be correctly examined and understood, is the Luminosity Function in young star-forming regions, where very low mass stars and brown dwarfs are more luminous, and the derivative of the ML relation, forM ≲, 0. 1 M⊙, is reasonably large, especially for ages 0. 2–1 × 107yr. I also discuss the recent H ST observations of the Globular cluster NGc 6397. The HR diagram of the main sequence presents a “double kink” shape, which can be theoretically understood. While the first kink (at MI ~ 7. 5) is already a well known feature both of stellar models and in the observations, the second kink (at MI ~ 10. 5) was predicted by theoretical models (D’Antona, 1987), but it has been observed here for the first time. As the kinks, the change of slope in the ML, and the corresponding presence of features in the LF are related, I suggest that they may be used as a powerful way to check consistency between the distance modulus and assumed chemistry of the system under study, before one finally derives the MF. In fact, the MF index depends on the adopted distance modulus. I finally suggest that the flattening of the disk MF at ~ 0. 2 M ⊙ and its sharp increase at the MS bottom may be due to strong mass loss in M dwarfs of Pop. I, which alters a monotonically increasing IMF.