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.