The atmospheres of low metallicity cool stars are composed primarily of hydrogen and helium. Collision-induced absorption by H 2 -H 2 and H 2 -He transient complexes will be a more or less important opacity source of their atmospheres. For example, CIA in the H 2 fundamental band, which falls on top of an opacity window between H 2 O/CH 4 or H 2 O/CO (depending on the temperature), plays an important role in shaping brown dwarf spectra. Higher gravity brown dwarf stars often show even stronger CIA, owing to the density squared dependence of CIA intensities, when other "ordinary" opacity sources are linearly dependent on density. CIA is also important in low-metallicity brown dwarfs, since "low metallicity" means reduced CNO (and other) elemental abundances compared to H 2 and He, and thus stronger CIA compared to H 2 O, CO, and CH 4 absorption. CIA absorption of H 2 -X collisional complexes is thus an important diagnostic of high-gravity and low-metallicity brown dwarfs. All of this is also true of the M dwarfs, but to a lesser extent. M dwarf atmospheres are hotter so that some increased portion of the H 2 molecules is in the dissociated state, which weakens CIA by H 2 --X complexes. The significance of CIA for cool astronomical objects was long suspected or known to some degree.