3.4. Star Formation Rate
One of the breakthrough due to recent progress on faint galaxies has been the inventory of the amount of star formation at every epoch (e.g. Madau et al. 1996). The comoving star formation rate is increasing like (1 + z)4 from z = 0 to z = 1, and then decreases again to the same present value down to z = 5. But this relies on the optical studies, i.e. on the UV-determined star forming rates in the rest-frame. If early starbursts are dusty, this decrease could be changed into a plateau (Guiderdoni et al. 1997, 1998; Blain et al. 1999c). Since the AGN-starbursts nature of the submm sources is still an open question, Trentham et al. (1999) consider two extreme possibilities: either the submm faint galaxies are all dusty starbursts, but even then, they do not dominate the star formation rate in the Madau plot at any redshift; or they are dusty AGN, and again they cannot represent more than a few percents of the present density of dark objects, as inferred by Magorrian et al. (1998).