Some of the key open questions in galaxy evolution are how gas flows into and out of galaxies, and how this gas gets converted into stars over time. A primary challenge in observing distant galaxies is that the light emitted by them is often too faint to allow detailed studies. Absorption lines in the spectra of background quasars can be used to probe gas in and around galaxies at various stages of evolution, and thus provide powerful probes of the history of star formation and chemical enrichment in galaxies. We have used this technique to track the build up of "metals" over the past ~11.5 billion years, uncovering both, a discrepancy relative to the models in the observed amount of metals in the more gas-rich galaxies, and a very high level of metals in the less gas-rich galaxies. We are now pushing the limits of this technique to reach galaxies in the first ~1 billion years after the Big Bang. Measurements of element abundances in this early epoch can help to constrain the initial mass function of the early generations of stars. Furthermore, spectra of gravitationally lensed quasars allow us to measure spatial variations in element abundances in the foreground galaxy. We have also succeeded in obtaining "3-D spectra" of some galaxies and measuring the flows of gas in and around them. We will discuss how all of these observations are helping to shed light on various aspects of galaxy evolution.