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The study of the molecular gas in quasars and submillimeter galaxies at high redshift has significantly progressed during the last few years. From the current detection of CO emission in 37 sources spanning a range in redshift from $1<z<6.4$ with, in some cases, the measurement of a series of CO rotational transitions, it is possible to constrain the physical conditions of the massive ($\ge 10^{10} \, M_\odot$) reservoirs of gas in these objects. This review will present the current status of the studies of molecular gas in high-$z$ sources, detail the physical conditions which pertain in these systems, which are scaled-up versions of the local ULIRGS, and discuss the searches in high-$z$ sources for species other than CO, including the fine structure lines of neutral carbon and the recent detection of the redshifted [CII] emission line in the $z=6.4$ quasar J 1148+5251. These results hold great promise for the study of galaxy formation and their evolution with redshift. This review will conclude by outlining the expected progress in the field, in particular when future instruments such as ALMA will be operational, which will enable to study the astrochemistry and its evolution in the early universe.
