I will describe the constraints available from a study of AGN evolution synthesis models on the growth of the SMBH population in the two main 'modes' observed (`kinetic-' and`radiatively-dominated', respectively). I'll show how it is possible to derive tight constraints on the Eddington ratio distribution of accreting black holes as a function both of BH mass and redshift. Thanks to this, it is possible to show that the SMBH mass function evolves anti-hierarchically, i.e. the most massive holes grew earlier and faster than less massive ones, similarly to what observed for star forming galaxies. Finally, I will present new constraints on the evolution of the black hole-galaxy scaling relation at 1