Abstract: Fully understanding the evolutionary state of a galaxy requires that we characterize its gas reservoir, of which the molecular component represents the mass directly available for star formation. I will discuss observations of molecular gas in two populations of star-forming galaxies at high redshift-- Lyman break galaxies and submillimeter galaxies-- and what we can conclude from them. Looking ahead to the future, I will outline what we can expect to learn from observations with two new instruments: the "Zpectrometer" (an ultrawide-bandwidth 26-40 GHz spectrometer for the 100m Green Bank Telescope) and ALMA (the Atacama Large Millimeter Array).