  The correlation between the photon energy at which the redshift corrected nFn
spectrum peaks (hence called "peak energy", Ep,i) and the isotropic equivalent
radiated energy (Eiso), is one of the most intriguing and debated observational
evidences in Gamma- Ray Bursts (GRB) astrophysics. In order to fully exploit
this correlation to understand GRB physics and use them as a cosmological tool,
we need to understand and reduce selection effects and biases in the sample of
GRBs with known redshift. The Swift satellite, thanks to its scientific payload
and unprecedented slewing capabilities, is providing us new observational
evidences and a reduction of selection effects in the process of GRB redshift
estimate. I discuss the location of Swift GRBs in the Ep,i-Eiso plane and the
main implications, with particular emphasis on selection effects, the existence
and nature of sub-energetic long GRBs, the GRB-SN connection, the difference
between long and short GRBs and the recently discovered sub-class of long GRBs
without association with a hypernova. I also briefly review the impact of Swift
observations on 3-parameters spectrum-energy correlations, which have been
proposed as a potentially powerful tool to standardize GRBs for the estimate of
cosmological parameters.
