  We review the relevance of H2 molecules for structure formation in cosmology.
Molecules are important at high redshifts, when the first collapsed structures
appear with typical temperatures of a few hundred Kelvin. In these chemically
pristine clouds, radiative cooling is dominated H2 molecules. As a result, H2
``astro-chemistry'' is likely to determine the epoch when the first
astrophysical objects appear. We summarize results of recent three-dimensional
simulations. A discussion of the effects of feedback, and implications for the
reionization of the universe is also given.
