With nearly one hundred gravitational-wave events observed by LIGO and Virgo, the mass spectrum of binary black holes starts revealing a number of features. While the most common primary black hole mass is about 8-10 Msun, the data reveal an excess at 35 Msun and a long tail extending out to 90 Msun. Such features must encode the formation history of binary black holes, but their analysis has brought us more questions than answers to date. In my talk, I discuss several possible scenarios for the emergence of these features, based on novel semi-analytic models of binary evolution and star cluster dynamics.