  Knowledge of the molecular component of the ISM is fundamental to understand
star formation. The H2 component appears to dominate the gas mass in the inner
parts of galaxies, while the HI component dominates in the outer parts.
Observation of the CO and other lines in normal and starburst galaxies have
questioned the CO-to-H2 conversion factor, and detection of CO in dwarfs have
shown how sensitive the conversion f actor is to metallicity. Our knowledge has
made great progress in recent years, because of sensitivity and spatial
resolution improvements. Large-scale CO maps of nearby galaxies are now
available, which extend our knowledge on global properties, radial gradients,
and spiral structure of the molecular ISM. Millimetric interferometers reveal
high velocity gradients in galaxy nuclei, and formation of embedded structures,
like bars within bars. Galaxy interactions are very effective to enhance gas
concentrations and trigger starbursts. Nuclear disks or rings are frequently
observed, that concentrate the star formation activity. Since the density of
starbursting galaxies is strongly increasing with redshift, the CO lines and
the mm dust emission are a privileged tool to follow evolution of galaxies and
observe the ISM dynamics at high redshift: they could give an answer about the
debated question of the star-formation history, since many massive remote
starbursts could be dust-enshrouded.
