I will present the final results of an extensive survey of GRB host galaxies, aimed at characterizing the optical and near-infrared properties of a carefully X-ray selected sample of 69 GRB hosts with 0.03 < z < 6.3. I will report on the detection rate, color distribution, Lyman alpha recovery fraction. Particular attention has been given to increase the redshift completeness by securing host redshifts (aided by the availability of the X-shooter spectrograph), leading to a remarkable 77% redshift completeness. We can thus constrain the redshift evolution of the GRB rate. Our survey allows testing the population of optically-undetected GRBs. Their hosts are on the average brighter and redder than those of optically-detected GRBs.