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The evolution of the content of heavy elements in galaxies, the relative chemical abundances, their spatial distribution, and how these scale with various galactic properties, provide unique information on the galactic evolutionary processes across the cosmic epochs. In recent years major progress has been made in constraining the chemical evolution of galaxies and inferring key information relevant to our understanding of the main mechanisms involved in galaxy evolution. In this review we provide an overview of these various areas. After an overview of the methods used to constrain the chemical enrichment in galaxies and their environment, we discuss the observed scaling relations between metallicity and galaxy properties, the observed relative chemical abundances, how the chemical elements are distributed within galaxies, and how these properties evolve across the cosmic epochs. We discuss how the various observational findings compare with the predictions from theoretical models and numerical cosmological simulations. Finally, we briefly discuss the open problems and the prospects for major progress in this field in the nearby future. [ABSTRACT FROM AUTHOR]