The handful of existing LIGO-Virgo detections will soon grow into an extensive catalog of compact binary coalescence events. With more events we can mine the statistics and demographics of the population in a bid to unveil the environments and evolutionary paths of progenitors. At lower frequencies, LISA will be sensitive to many massive black-hole mergers, with a catalog of such events offering insight into black-hole seed formation scenarios and accretion processes. Finally, at nanohertz frequencies, the superposition of gravitational wave signals from many inspiraling supermassive black-hole binaries is helping to constrain black-hole—host-galaxy scaling relationships, and the dynamical environments of host galaxy centers. I will outline a general statistical framework wherein detailed models for gravitational-wave population demographics can be constructed using insight from sophisticated population synthesis simulations. These models are deployed in hierarchical Bayesian analysis to recover joint posterior probability distributions of progenitor properties, evolutionary paths, and dynamical interactions. The end result is a family tree for the detected gravitational-wave populations, and new probes of the physical processes guiding their formation.