Published online by Cambridge University Press: 27 October 2016
The bright-end cutoff of the [O III] λ5007 planetary nebula luminosity function (PNLF) is insensitive to population age and metallicity, making it an excellent extragalactic standard candle. We review our knowledge of the function and discuss the challenges related to modeling it. We show that, while there has been a great deal of progress in understanding the nuances of its shape, there is still no solid theory which explains the luminosity of the PNLF cutoff in old stellar populations. This is an extremely serious problem, as it affects a myriad of astrophysical issues, from the determination of the stellar masses of galaxies to our understanding of alternative channels of stellar evolution.