The lives of star clusters are inextricably linked to the assembly and evolution of their parent galaxies. While significant progress has been made in understanding galaxy formation and the dynamics of star clusters as separate systems, our understanding of their symbiotic connection remains in its infancy. In this talk, I will describe how we model dense star clusters, both analytically and numerically, and what motivates our typical choices of initial conditions. I will demonstrate how massive and old clusters, such as the globular clusters in the Milky Way, are an ideal site for the production of heavy binary black holes, and how repeated binary mergers in these environments can produce black hole masses that cannot be explained though the collapse of single stars. I will then describe a recent project to model these 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 formed from isolated binaries and dense star clusters, including GW190412 and GW190521, two recent gravitational-wave detections with unique masses and spins.