All the heavy elements in the universe are formed by massive stars within galaxies. These heavy elements are recycled back into the interstellar medium of galaxies via stellar winds and supernovae. Observations of nebular emission allow us to measure the abundance of heavy elements in the gas-phase out to high redshifts. These observations provide important constraints for gas flows in and out of galaxies and star formation, key processes governing the evolution of galaxies. I will discuss the history of observations and methods used in determining the chemical evolution of galaxies. I will present recent advances, some outstanding problems in our understanding of the chemical evolution of galaxies and potential solutions to these problems. I will conclude by showing how measurements of heavy element abundances are being used to understand the fundamental physical processes governing galaxy evolution.