  The measurement of chemical abundances in planetary nebulae in nearby
galaxies is now relatively straightforward. The challenge is to use these
chemical abundances to infer the chemical evolution of their host galaxies. At
this point, our understanding of chemical evolution based upon planetary
nebulae in galaxies without star formation is strongly coupled to our
understanding of the relationship between the chemical abundances in stars and
planetary nebulae in the Milky Way bulge. Supposing that the same relation
holds in all systems where star formation ceased long ago, these systems follow
a metallicity-luminosity relation that is displaced to higher chemical
abundances compared to that found for dwarf irregular galaxies. A more
efficient enrichment process appears to be required as part of the explanation
for this shift, in addition to the inevitable fading of these galaxies.
