  These are exciting times for binary black hole (BBH) research. LIGO and Virgo
detections are progressively drawing a spectacular fresco of BBH masses, spins
and merger rates. In this review, we discuss the main formation channels of
BBHs from stellar evolution and dynamics. Uncertainties on massive star
evolution (e.g., stellar winds, rotation, overshooting and nuclear reaction
rates), core-collapse supernovae and pair instability still hamper our
comprehension of the mass spectrum and spin distribution of black holes (BHs),
but substantial progress has been done in the field over the last few years. On
top of this, the efficiency of mass transfer in a binary system and the physics
of common envelope substantially affect the final BBH demography. Dynamical
processes in dense stellar systems can trigger the formation of BHs in the mass
gap and intermediate-mass BHs via hierarchical BH mergers and via multiple
stellar collisions. Finally, we discuss the importance of reconstructing the
cosmic evolution of BBHs.
