Black hole demography at the dawn of gravitational-wave astronomy: state of the art and future perspectives

The first LIGO-Virgo detections have confirmed the existence of massive black holes (BHs), with mass $30-40$ M$_odot$. Such BHs might originate from massive metal-poor stars ($Z<0.3$ Z$_odot$) or from gravitational instabilities in the early Universe. The formation channels of merging BHs are still poorly constrained. The measure of mass, spin and redshift distribution of merging BHs will give us fundamental clues to distinguish between different models. Also, a better understanding of several astrophysical processes (e.g. common envelope, core-collapse supernovae, and dynamical evolution of BHs) is decisive, to shed light on the formation channels of merging BHs.