Astronomical observations can effectively probe in space-time the variability of the physical dimensionless constants such as the fine structure constant alpha and proton-to-electron mass ratio which are related to fundamental forces of nature. Several theories beyond the SM allow for varying constants and there is a possible connection with dark energy if due to quintessence. Current astronomical observations and claims on the possible variability of the fine structure and of the electron-to-mass ratio will be critically reviewed trying to understand the controversial results obtained. The proposal for the ESPRESSO (Echelle Spectrograph for Precision Super Stable Observations) spectrograph at the combined incoherent focus of the 4 ESO-VLT units (a potential 16 m equivalent telescope) and its follow up for the E-ELT CODEX (COsmic Dynamics EXperiment) will be briefly described . These instruments, if realized, will make possible a significant improvement, thus solving the present controversy and opening a new field of research in case positive results are provided.