It becomes possible now to detect cold molecules at high redshift in the millimeter domain. Since the first discovery in 1992 by Brown and van den Bout of CO lines atz=2.28in a gravitationally lensed starburst galaxy, nearly ten objects are now known to possess large quantities of molecular gas beyondz=1and up toz∼5,through millimeter and sub-millimeter emission lines. Even more objects have been detected in their continuum dust emission, and a few galaxies through millimeter absorption lines in front of quasars atz⩽1.The continuum dust emission is the most easily detected: for a starburst dust atTd∼60&hthinsp;K,the emission peaks around 60 &mgr;m, and falls as&lgr;−4at longer wavelengths. In the mm domain, the emission is then stronger for the more redshifted objects. For the CO lines, the situation is less favorable, and the reported detections are helped by gravitational amplification. The increase of the CMB temperatureTbgwith redshift helps the rotational line excitation (especially at highz), but not its detection. Absorption in front of quasars is a more sensitive probe of cold gas at high redshift, able to detect individual clouds of a few solar masses (instead of1010&hthinsp;M⊙for emission). Taking advantage of the small size of the QSO, very high spatial resolution (of the order of milli-arcsec) can be achieved, and high spectral (30 m/s) resolution, due to the heterodyne technique. The sampled column-densities range betweenN(H2)=1020et1024&hthinsp;cm−2.The high sensitivity allows to detect a multitude of molecular lines in a single object (HCO+,HNC, HCN,N2H+,C18O,CS,H2CO,CN, CCH,H2Setc&ellip;.), and compare the chemistry with the local one, atz=0.From the diffuse components, one can measure the cosmic black body temperature as a function of redshift. The high column densities component allow to observe important molecules not observable from the ground, likeO2,H2Oand LiH for example. All these preliminary studies carry a great hope for what will be observed with future millimeter instruments, and some perspectives are given. ©1999 American Institute of Physics.