The Cosmic Background due to the integrated radiation from galaxies over the whole life of the Universe is reviewed .
We find that this background is well constrained by measurements .
The total power in the background is in the range 60-93 nWm ^ { -2 } sr ^ { -1 } .
The data show the existence of a minimum separating the direct stellar radiation from the infrared part due to radiation reemitted by dust .
This reemitted dust radiation is about 1-2.6 time the background power in the optical/near-IR thus much larger than the same ratio measured locally ( 30 \% ) .
The far-infrared and submillimeter background is likely to be dominated by redshifted infrared galaxies .
The long wavelength spectrum of the background being significantly flatter than the spectrum of these galaxies it strongly constrains the far-infrared radiation production rate history which must increase by a factor larger than 10 between the present time and a redshift 1 and then stays rather constant at higher redshift , contrary to the ultraviolet radiation production rate which decreases rapidly .

Several models of galaxy evolution have been proposed to explain the submillimeter background .
In this paper we do not propose a new model ; we systematically explore the allowed range of evolution histories allowed by the data .
If infrared galaxies are mostly powered by starbursts as indicated by recent observations , this infrared production history reflects the history of star formation in the Universe .