CODEX, a high resolution, super-stable spectrograph to be fed by the E-ELT, the most powerful telescope ever conceived, will for the first time provide the possibility of directly measuring the change of the expansion rate of the Universe with time and much more, from the variability of fundamental constants to the search for other earths. A study for the implementation at the VLT of a precursor of CODEX, dubbed ESPRESSO, is presently carried out by a collaboration including ESO, IAC, INAF, IoA Cambridge and Observatoire de Geneve. The present talk is focused on the cosmological aspects of the experiment.