With Herschel, we have been able to follow the evolution of the cosmic star formation history
to z ~ 4. We will present the main results from this work. However, this is not the end of the 
story and we would like to better understand what happens at z ~ 3-4 and extends this to higher 
redshifts. The main population of high redshift objects are Lyman break galaxies (LBGs). 
So, the first step is to really understand what are the characteristics of LBGs at z ~ 3-4. 
We present the results of a study of the far-infrared (rest-frame) properties of z ~ 3 LBGs, 
based on Herschel (PACS and SPIRE) and AzTEC observations in COSMOS. We have used a stacking analysis 
to characterize the properties of LBGs, because (statistically) they cannot be detected individually. 
We have selected 15.600 LBGs. This is the largest sample used to do this kind of work up to now
and we have determined the properties of our sample as a function of the FUV luminosity, the stellar 
mass and the UV slope. To understand these galaxies, we have and still are developing a code name CIGALE 
to analyse SEDs and to create galaxy modelled spectra. We will also present a new code to study the 
chemical evolution of galaxies and to predict the line emission at all redshfts. Finally, we will present 
a French/European possible contribution to a new Japanese-led project (WISH) to study the very high 
redshift universe.