Weak lensing at the limit of the sky background noise

Recent weak lensing observations have pushed the use of 4 meter-class telescopes to the limits of their capabilities with exposure times exceeding several hours. The leading idea is that the surface density of faint galaxies up to very faint magnitude ($B > 28-30$) raises continuously thus potentially offering a dense template of distant sources whose intensity contrast is at the sky noise level. In complement to the Peter Schneider's presentation on dark matter search from weak lensing (this conference), we review some of these recent advances in weak lensing analysis based on this extreme faint population of galaxies in order to explore: the dark matter distribution on large scales, the redshift ditribution of lensed sources at very large distance, and eventually the values of cosmological parameters. For each observational topic we will briefly discuss these new methods as compare to more classical lensing studies as well as the possible VLT scientific impact in the domain.