AbstractWe compute the luminosity function (LF) and the formation rate of long gamma ray bursts (GRBs) in three different scenarios: i) GRBs follow the cosmic star formation and their LF is constant in time; ii) GRBs follow the cosmic star formation but the LF varies with redshift; iii) GRBs form preferentially in low–metallicity environments. We then test model predictions against the Swift 3-year data, showing that scenario i) is robustly ruled out. Moreover, we show that the number of bright GRBs detected by Swift suggests that GRBs should have experienced some sort of luminosity evolution with redshift, being more luminous in the past. Finally we propose to use the observations of the afterglow spectrum of GRBs at z ≥ 5.5 to constrain the reionization history, and then applied our method to the case of GRB 050904.