Black hole demography: from scaling relations to models

In this contributed paper, I review our current knowledge of the local black hole (BH) scaling relations and their impact on the determination of the local BH mass function. I particularly emphasize the remaining systematic uncertainties impinging upon a secure determination of the BH mass function and how progress can be made in this direction. I then review and discuss the evidence for a different time evolution for separate BH-galaxy scaling relations, and how these independent empirical evidences can be reconciled with the overall evolution of the structural properties of the host galaxies. I conclude discussing BH demography in the context of semi-empirical continuity accretion models, as well as more complex evolutionary models, emphasizing the general constraints we can set on them.