We generally assume our Universe has a set of constants that hold true through space and time, but these parameters can only be measured. There is no reason besides simplicity that we should consider them constant. Testing their constancy is in itself a test of the theories where they are used. They allow us to test the domain of their validity and if their constancy doesn’t hold true to expand our knowledge. Absorption lines produced by the intervening clouds along the line of sight of the QSO give access to physical information on the atoms/molecules present in the cloud. Comparing tiny variations of the position of some lines with respect to other reference lines we can test the stability of the fine-structure constant or the proton-to-electron mass ratio. Indeed there is a claim (Webb et al 2012) of a redshift and dipole variation of fine-structure constant at about 10 ppm level using high-resolution spectra of about 300 absorption clouds. But we know that those observations were probably dominated by latter discovered systematics. In this talk, I will describe the complexity of the methods used to measure fundamental constants using QSOs and the current state of the field. And I will present how ESPRESSO, the new high- resolution spectrograph for VLT will be able to perform systematics free measurements and put strict bounds on the existing dipole claim.