Chemical abundances provide important clues to the evolution of galaxies. Ionized nebulae are one of the main sources of chemical abundance measurements, especially in external galaxies. Studies of H II regions have shown that the overall metallicity of galaxies increases with galactic luminosity, and that spiral galaxies characteristically have radial gradients in chemical composition. There are indications of environmental influences on chemical abundances. Planetary nebulae provide another measure of abundances in the Milky Way and other galaxies. Space facilities have allowed measurements for elements that are inaccessible at optical wavelengths. Large telescopes make possible the study of individual stars in external galaxies and the study of interstellar abundances in galaxies at intermediate and high redshifts. These advances promise exciting times as astrophysicists strive to paint a complete picture of galactic evolution from the Big Bang to the present.

6 pages LATEX; uses rmaa.cls and rmaacite.sty (included). To appear in "Ionized Gaseous Nebulae", ed. William Henney et al., RevMexAA (Serie de Conferencias), in press (2001)