  The prompt emission mechanism of gamma-ray bursts (GRB) even after several
decades remains a mystery. However, it is believed that correlations between
observable GRB properties given their huge luminosity/radiated energy and
redshift distribution extending up to at least $z \approx 9$, are promising
possible cosmological tools. They also may help to discriminate among the most
plausible theoretical models. Nowadays, the objective is to make GRBs standard
candles, similar to supernovae (SNe) Ia, through well-established and robust
correlations. However, differently from SNe Ia, GRBs span over several order of
magnitude in their energetics and hence cannot yet be considered standard
candles. Additionally, being observed at very large distances their physical
properties are affected by selection biases, the so called Malmquist bias or
Eddington effect. We describe the state of the art on how GRB prompt
correlations are corrected for these selection biases in order to employ them
as redshift estimators and cosmological tools. We stress that only after an
appropriate evaluation and correction for these effects, the GRB correlations
can be used to discriminate among the theoretical models of prompt emission, to
estimate the cosmological parameters and to serve as distance indicators via
redshift estimation.
