Currently, we know of more than 50 compact binary mergers from the first observation runs of LIGO and Virgo, and expect a "deluge" of new detections in the next few years. This wealth of new data provides us with crucial insight on the populations of binary compact objects, helping us to tackle some of the main open questions: What is the mass function of compact objects? What is the distribution of black hole spins? What are the formation channels of binary compact objects? However, the predictive power of astrophysical models is hampered by multiple uncertainties, regarding the evolution of massive binary stars, the fate of core-collapse supernovae, the dynamics of stellar clusters and the evolution of star formation across cosmic times. In this talk, I will review the state-of-the-art of astrophysical models of binary compact objects, and discuss the main actions theoretical astrophysicists need to take to be ready for the scientific exploitation of third-generation gravitational-wave detectors.
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