I will review some recent results about the molecular content of galaxies and its dynamics, obtained from CO lines, dense tracers (HCN,HCO+), or the dust continuum emission. New data to constrain the conversion factor XCO will be discussed. The molecular surface density is essential to determine the star formation efficiency in galaxies, and the resolved Kennicutt-Schmidt law will be presented as a function of surface density and galaxy type. Large progress has been made on galaxy at moderate and high redshifts, allowing to interprete the star formation history and star formation efficiency as a function of gas content, or galaxy evolution. In massive galaxies, the gas fraction was higher in the past, and galaxy disks were more unstable and more turbulent. ALMA observations will allow the study of more normal galaxies at high z with higher spatial resolution and sensitivity.