Explore the latest insights on binary compact objects in this 41-minute lecture by Michela Mapelli from the University of Padova. Delve into the astrophysical models, open questions, and main uncertainties surrounding compact binary mergers as observed by LIGO and Virgo. Gain a comprehensive understanding of the mass function of compact objects, black hole spin distributions, and formation channels of binary compact objects. Examine the challenges faced by astrophysical models, including the evolution of massive binary stars, core-collapse supernovae, stellar cluster dynamics, and cosmic star formation evolution. Learn about the current state of astrophysical models and the necessary steps for theoretical astrophysicists to prepare for third-generation gravitational-wave detectors. The lecture covers topics such as neutron star and black hole masses, isolated binary evolution, spin distributions, dynamics, and future challenges in the field of gravitational wave astronomy.