In the context of future Herschel observations in the far-infrared, I will show how the star-formation activity can be efficiently measured in the distant universe, up to redshift 5. I shall present two approaches for this purpose: direct measurements of luminosity functions from deep surveys on the one hand, and indirect constraints from multi-wavelength/multi-scales galaxy counts on the other hand. These works use data from the mid-infrared (Spitzer) to the sub-millimeter (SCUBA) and will benefit greatly from future Herschel programs.
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