The Evolution of Gas and Star Formation from z=3 to z=0
  The cosmic star formation rate density first increases with time towards a
pronounced peak 10 Gyrs ago (or z=1-2) and then slows down, dropping by more
than a factor 10 since z=1. The processes at the origin of the star formation
quenching are not yet well identified, either the gas is expelled by supernovae
and AGN feedback, or prevented to inflow. Morphological transformation or
environment effects are also invoked. Recent IRAM/NOEMA and ALMA results are
reviewed about the molecular content of galaxies and its dynamics, as a
function of redshift. Along the main sequence of massive star forming galaxies,
the gas fraction was higher in the past (up to 80\%), and galaxy disks were
more unstable and more turbulent.
  The star formation efficiency increases with redshift, or equivalently the
depletion time decreases, whatever the position of galaxies, either on the main
sequence or above. Attempts have been made to determine the cosmic evolution of
the H_2 density, but deeper ALMA observations are needed to effectively compare
with models.
