https://zoom.us/j/97377192005?pwd=OUZPR1Z3ZGc5WDZPYW1SakEzV1pvQT09 The latest results from the LIGO-Virgo-KAGRA collaboration draw a spectacular fresco of binary black hole mergers, ranging from a few to more than hundred solar masses. In this talk, I will discuss the main astrophysical formation channels of binary black holes, highlighting the open questions. On the one hand, models of stellar evolution and pair instability suggest the existence of a gap in the mass spectrum of black holes between ~60 and ~120 solar masses. The boundaries of this gap drastically depend on massive star evolution and on the efficiency of envelope removal during core collapse. On the other hand, extreme dynamical processes in dense star clusters can fill the mass gap, via multiple stellar collisions, dynamical exchanges and hierarchical mergers. These processes might build up intermediate-mass black holes with mass up to several thousand solar masses, especially in the most metal-poor and massive clusters. The evolution of such dynamical mergers across cosmic time will be one of the most exciting targets of next-generation ground-based detectors. Prof. Mapelli is being hosted by Prof. Ralf Klessen of the ITA institute (klessen@uni-heidelberg.de). Anyone interested in further discussions on specific topics should contact Prof. Klessen to arrange (virtual) follow-up meetings with Prof. Mapelli