Luminosity functions of planetary nebulae contain information about the central star mass distributions, nebular, central star, and progenitor evolution, stellar death rates, and a galaxy's star formation and chemical evolution histories. Appropriate observing strategies can be used in combination with various models to extract some of the parameters of these functions. The principal results from these studies are that the central star mass distribution is narrow (σ ∼ 0.02–0.04M
⊙), the number of PN in a galaxy depends on galaxy color, and the number of PN in the Galaxy is ∼ 104.
The most extensive application of luminosity function studies has been exploiting the bright end cutoff as a distance indicator. Distances for 25 galaxies have been measured using the methodology outlined by Jacoby, Ciardullo, and collaborators. The PNLF method compares extremely well with other techniques, and is accurate to ∼ 5%. In fact, there is no evidence for systematic effects of any kind, although a small (5–10%) metallicity correction needs to be applied for metal-poor systems.