Since 2015, LIGO and Virgo have detected nearly 50 gravitational waves from merging black holes and neutron stars, ushering in a new era of observational astronomy. But how are the binary progenitors of these systems actually formed in the first place? In this talk, I will attempt to answer that question, by describing how massive and old star clusters, such as the globular clusters in the Milky Way, are an ideal site for the production of binary black holes. I will show how unique features of these dense stellar environments directly influence the gravitational waveforms themselves, and how repeated binary mergers in clusters produce black hole masses that cannot be explained though normal stellar evolutionary processes. I will then describe a recent project to model star clusters self-consistently from collapsing giant molecular clouds in an MHD simulation of a Milky Way-sized galaxy. Finally, I will connect these results to the binary black holes detected by LIGO/Virgo, including GW190412 and GW190521, two recently reported gravitational-wave detections with unique masses and spins.