  In a few dozen seconds gamma ray bursts (GRBs) emit up to 10^54 erg in terms
of an equivalent isotropically radiated energy Eiso, so they can be observed up
to z ~10. Thus, these phenomena appear to be very promising tools to describe
the expansion rate history of the universe. Here we review the use of the Ep,i
- Eiso correlation of GRBs to measure the cosmological density parameter
Omega_M. We show that the present data set of Gamma-Ray Bursts, coupled with
the assumption that we live in a flat universe, can provide independent
evidence, from other probes, that Omega_M ~0.3. We show that current (e.g.,
Swift, Fermi/GBM, Konus-WIND) and forthcoming GRB experiments (e.g., CALET/GBM,
SVOM, Lomonosov/UFFO, LOFT/WFM) will allow us to constrain Omega_M with an
accuracy comparable to that currently exhibited by Type Ia supernovae and to
study the properties of dark energy and their evolution with time.
