Characterizing the relationship between stars, gas, and metals in galaxies is a critical component of understanding the cosmic baryon cycle. We compile contemporary censuses of the baryons in collapsed structures and their chemical make-up and dust content. We show the following: ▪ The HI mass density of the Universe is well determined to redshifts z≈5 and shows minor evolution with time. New observations of molecular hydrogen reveal its evolution mirrors that of the global star-formation rate density, implying a universal cosmic molecular gas depletion timescale. The low-redshift decline of the star-formation history is thus driven by the lack of molecular gas supply due to a drop in net accretion rate related to the decreased growth of dark matter halos. ▪ The metal mass density in cold gas ( T≲104 K) contains virtually all the metals produced by stars for z≳2.5. At lower redshifts, the contributors to the total amount of metals are more diverse; at z < 1, most of the observed metals are bound in stars. Overall, there is little evidence for a “missing metals problem” in modern censuses. ▪ We characterize the dust content of neutral gas over cosmic time, finding the dust-to-gas and dust-to-metals ratios fall with decreasing metallicity. We calculate the cosmological dust mass density in the neutral gas up to z≈5. There is good agreement between multiple tracers of the dust content of the Universe. Expected final online publication date for the Annual Review of Astronomy and Astrophysics, Volume 58 is August 18, 2020. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.