We review here the main direct or indirect ways to detect the possible
presence of large amounts of cold molecular hydrogen in the outer par
ts of disk galaxies, an hypothesis that we have recently developed. Di
rect ways range from H-2 absorption in the UV domain to detection of t
he radio hyperfine structure: the ortho-H-2 molecule has an hyperfine,
or ultrafine, structure in its fundamental state, due to the coupling
between the rotation-induced magnetic moment, and the nuclear spin. T
his gives rise to 2 magnetic dipole transitions, at the wavelengths of
0.5 and 5.5 km. Indirect ways are essentially the detection of the HD
and LIH transitions, and in some environments like clusters of galaxi
es, more heavy trace molecules such as CO. We discuss from this point
of view the recent discovery by COBE/FIRAS of a very cold Galactic dus
t component (4 - 7 K) which could correspond to a dominating gas mass
component of the ISM, if interpreted as standard dust emission. Some o
f the proposed means could be applied to the well-known molecular clou
ds, to bring some new light to the problem of the H-2/CO conversion ra
tio.