Explore the fascinating world of merging black-hole binaries in this comprehensive astrophysics colloquium talk. Delve into the recent breakthroughs in gravitational wave detection by advanced LIGO/Virgo and their implications for understanding the formation mechanisms of merging compact binaries. Examine various aspects of dynamical formation channels, with a focus on tertiary-induced mergers and AGN disks. Learn how observations of spin-orbit misalignments, eccentricities, masses, and mass ratios in merging binary samples can constrain these formation channels. Discover novel three-body dynamical effects related to merging binaries. Gain insights from expert speaker Dong Lai of the Institute for Advanced Study as he presents cutting-edge research in this hour-long lecture, part of the Institute for Advanced Study / Princeton University Joint Astrophysics Colloquium series.