  Studies of the molecular interstellar medium that fuels star formation and
supermassive black hole growth in galaxies at cosmological distances have
undergone tremendous progress over the past few years. Based on the detection
of molecular gas in >120 galaxies at z=1 to 6.4, we have obtained detailed
insight on how the amount and physical properties of this material in a galaxy
are connected to its current star formation rate over a range of galaxy
populations. Studies of the gas dynamics and morphology at high spatial
resolution allow us to distinguish between gas-rich mergers in different stages
along the "merger sequence" and disk galaxies. Observations of the most massive
gas-rich starburst galaxies out to z>5 provide insight into the role of cosmic
environment for the early growth of present-day massive spheroidal galaxies.
Large-area submillimeter surveys have revealed a rare population of extremely
far-infrared-luminous gas-rich high-redshift objects, which is dominated by
strongly lensed, massive starburst galaxies. These discoveries have greatly
improved our understanding of the role of molecular gas in the evolution of
massive galaxies through cosmic time.
