The ionization of galaxies by their planetary nebulae

Recent studies have shown that nuclei of planetary nebulae and their remnants (dubbed HOLMES for ``hot low-mass evolved stars'') can easily explain two long-standing problems of extragalactic astronomy: the observed emission-line spectra of ellipticals and LINER-like galaxies and the ionization and heating of the diffuse interstellar medium in spirals. They are summarized in this contribution. It is emphasized that the computation of grids of stellar evolution models until the white dwarf stage is essential not only for the study of planetary nebulae but also for the study of the ionization of galaxies.