The interstellar medium (ISM) is an essential ingredient of star and planet formation, and plays a key role in galactic evolution through its metal content. This PhD thesis is focused on understanding the gas and dust within the ISM of galaxies, both distant and in the Milky Way. By studying the chemical composition of gas in galaxies, we can learn more about how galaxies evolve over time. In this thesis I use high-resolution absorption-line spectroscopy to study the chemical enrichment and variation between individual gas clouds (or groups of clouds) within galaxies, both in the distant Universe and in the Milky Way. Absorption-line spectroscopy is particularly powerful for studying the metals in the ISM because it provides key information on many chemical elements, including their column densities and kinematics. Because metal absorption lines are typically narrow, they can be decomposed into their contributing components along the line of sight and therefore studied on a component-by-component basis, provided the spectral resolution is high enough. Most absorption-line spectroscopy research on the ISM has so far centered on examining the global properties of galaxies along the full line of sight. In this thesis I focus on the chemical properties of, and variations between, individual gas clouds within galaxies using dust depletion as a proxy for chemical enrichment. Dust depletion is the phenomenon whereby metals are missing from the gas phase because they are instead locked into dust grains. Different metals are incorporated into dust at different rates, which, using the relative abundances of metals with different refractory properties, can be used to determine the level of dust depletion in a gas system. This is called the relative method of characterising dust depletion. In my first paper, we develop the relative method to be applicable to this component-by-component analysis (i.e. regardless of H) and uncover variations in the level of dust depletion within 64 galaxies observed in absorption at redshifts 1.7 < z < 4.2. These results show that the galaxies are chemically complex, even in the early Universe. In my second paper, we characterise the chemical enrichment in individual gas components along eight lines of sight towards bright O/B-type stars within 1.5 kpc of the Sun using high resolution HST/STIS spectra from my program (ID: 16750, co-PI: Ramburuth-Hurt). We find variations in the level of dust depletion and show that these chemical intricacies on the component-by-component level are washed away by typical full line-of-sight analyses. We also constrain the metallicities of individual components, up to 0.3 dex in some cases, by simulating many scenarios of the hydrogen gas distribution between components along each line of sight. In my third paper, we compare two different probes of dust, depletion and extinction, by combining the results from my second paper and three-dimensional dust maps, allowing us to pinpoint the likely locations of the gas clouds by cross-matching the dust depletion components with the dust extinction distributions. This PhD work has contributed valuable methodologies and results to detailed studies on the metal and dust content of the ISM of galaxies, both far and near, and shown that the gas in galaxies is chemically complex. Looking forward, these component-by-component analyses make it possible to quantify these complexities for more of the ISM in more galaxies.