Since the first detection over three years ago, gravitational waves have promised to revolutionize our understanding of compact objects, binary evolution, general relativity, and cosmology. But to make that a reality, we need to understand how and where these relativistic binaries form. In this talk, I will describe the various astrophysical pathways for creating the binary mergers detected by LIGO/Virgo, and how specific features of the gravitational waves (such as the binary eccentricities and black hole spins) can shed light on the formation of these dark remnants. I will show how simple gravitational dynamics makes the centers of dense star clusters, particularly globular clusters, uniquely efficient at producing merging binaries. Finally, I will talk about the future of the field, and how gravitational-wave astronomy is poised to offer us unprecedented insights into physics, astrophysics, and cosmology over the coming years and decades.