  Recent observations with the IRAM instruments have allowed to explore the
star formation efficiency in galaxies as a function of redshift, in detecting
and mapping their molecular gas. Some galaxies stand on what is called the
"main sequence", forming stars with a rate that can be sustained over
time-scales of 1 Gyr, some are starbursts, with a much shorter depletion time.
Star formation was more active in the past, partly because galaxies contained a
larger gas fraction, and also because the star formation efficiency was higher.
The global Kennicutt-Schmidt relation was however similar until z \sim 2.5.
Magnification by gravitational lenses have been used to explore in details
galaxies at higher redshift up to 6. Herschel has discovered many of these
candidates, and their redshift has been determined through the CO lines. ALMA
is beginning to extend considerably these redshift searches, with its
broad-band receivers, for a large range of objects too obscured to be seen in
the optical.
