Over the last decade, observations of the cool interstellar medium in distant galaxies via molecular and atomic fine structure line emission has gone from a curious look into a few extreme, rare objects, to a mainstream tool to study galaxy formation, out to the highest redshifts. Molecular gas has now been observed in close to 200 galaxies at z > 1, including numerous AGN hostgalaxies out to z ∼ 7, highly starforming sub-millimeter galaxies (median redshift z ∼ 2.5), and increasing samples of 'main-sequence' color-selected star forming galaxies at z∼1.5-2.5. Studies have moved well beyond simple detections, to dynamical imaging at kpc-scale resolution, and multi-line, multi-species studies that determine the physical conditions in the interstellar medium in early galaxies. Observations of the cool gas are the required complement to studies of the stellar density and star formation history of the Universe, as they reveal the phase of the interstellar medium that immediately preceeds star formation in galaxies. Current observations suggest that the order of magnitude increase in the cosmic star formation rate density from z ∼ 0 to 2 is commensurate with a similar increase in the gas to stellar mass ratio in star forming disk galaxies. Progress has been made on determining the CO luminosity to H2 mass conversion factor at high-z, and the dicotomy between high versus low values for main sequence versus starburst galaxies, respectively, appears to persist with increasing redshift, with a likely dependence on metallicity and other local physical conditions. Studies of atomic fine structure line emission are rapidly progressing, with some tens of galaxies detected in the exceptionally bright [C II] 158µm line to date. The [C II] line is proving to be a unique tracer of galaxy dynamics in the early Universe, and, together with other atomic fine structure lines, has the potential to be the most direct means of obtaining spectroscopic redshifts for the first galaxies during cosmic reionization.