Observations of compact object mergers with gravitational waves help to reveal vital information about their progenitor stellar systems, such as the types of galactic environments they were born in, the intricacies of stellar evolution that persisted throughout their lives, and the physics of the supernovae that marked their deaths. In this talk, I will highlight a number of ways that the deluge of gravitational-wave observations helps to elucidate the environments where compact binaries merge and the veiled physical processes that embed binary stellar evolution. In particular, I will discuss how the diversity of compact object merger properties hint at multiple prominent formation channels contributing to the full population, the astrophysical implications of detecting systems with identifiable orbital eccentricity, and how the host demographics of both gamma-ray bursts and multimessenger events can help to unveil crucial aspects detailing the late phases of massive-star binary evolution.