  In order to understand galaxy evolution through cosmic times it is critical
to derive the properties of the molecular gas content of galaxies, i.e. the
material out of which stars ultimately form. The last decade has seen rapid
progress in this area, with the detection of massive molecular gas reservoirs
at high redshifts in submillimeter-selected galaxies and quasars. In the latter
case, molecular gas reservoirs have been quantified out to redshifts z>6, i.e.
towards the end of cosmic reionization when the universe was less than one Gyr
old. The recent discovery of molecular gas in more normal galaxies have
extended these studies from the most extreme objects in the universe
(SFR~1000M_sun/yr; quasars and submillimeter galaxies) to more 'normal'
starforming systems at redshifts 1.5-2.5 (with SFR~100M_sun/yr). However,
detecting the molecular gas reservoirs of high-redshift galaxies that only have
moderate star formation rates (~<10 M_sun/yr, similar to the faint galaxies
seen in the Hubble Ultra Deep Field) will likely have to await the completion
of ALMA.
