Gamma–Ray Bursts (GRBs) are potentially a very powerful tool for the measure of cosmological parameters. Indeed, they are the brightest sources in the universe (up to more than 1054 erg/s released in a few tens of s), their redshift distribution extends from about 0.1 to at least 6.7, and they radiate mostly in the hard X–ray band, thus avoiding, e.g., the dust extinction problems affecting type Ia SNe. However, the luminosities of GRBs span several orders of magnitude, thus a way to “standardize” them in a way similar, e.g., to what is done with type Ia SNe has to be found. Under this respect, the most promising and discussed tool is the correlation between the photon energy, Ep,i, at which the νFν spectrum peaks and the GRB radiated energy (Eiso) or luminosity (Liso, Lp,iso). By studying the scatter of these spectrum–energy correlations as a function of the adopted cosmology it is possible, with the present sample of ~80 GRBs with known redshift and spectral parameters, to derive, for a flat universe, significant constraints on ΩM consistent with the “concordance” cosmology value. Moreover, simulations show that, with the enlargement of the sample expected by present and future missions (Swift, GLAST/GBM, Konus–WIND, SVOM) it will be possible to simultaneously constrain both ΩM and ΩΛ, and, possibly, obtain information on the equation of state of dark energy and its evolution.