Compact object transients, from fast X-ray transients (FXTs) to gravitational wave (GW) detections, encode the astrophysical conditions required to produce them. In this talk, I present two complementary studies unified by a central question: how do these conditions shape the populations we observe and what they can reveal? First, I examine FXTs: brief, luminous X-ray flashes with uncertain origins. A proposed channel invokes the rapid spindown of nascent millisecond magnetars formed in binary neutron star mergers. By estimating the maximum formation rate of such magnetars across all plausible channels, we test whether they can explain the observed FXT population. We find that only a small fraction of neutron stars achieve the required spin and magnetic field strengths, allowing millisecond magnetars to account for $\sim$10% of FXTs; this illustrates how population-level rate arguments can constrain transient progenitor models. Second, I investigate binary black hole (BBH) mergers, which usually act as dark sirens. Using simulations of BBH mergers in nearby galaxies and future GW detector networks (including LIGO-India, CE, and ET), we compute 3D localization volumes using the Fisher-Information Matrix approximation, and compare them to theoretical limits derived from galaxy stellar mass functions of different BBH formation channels, metallicity-informed formation models, stellar mass fractions, and 3D p-chance. Next-generation networks routinely achieve volumes smaller than these thresholds, implying that host galaxy associations may be achievable out to $\sim1000$ Mpc, at a rate of $\sim 100~yr^{-1}$. This establishes a framework to directly connect BBH mergers to their progenitor environments and formation channels. Together, these results show how combining formation physics, population modeling, and detector capabilities enables strong constraints on progenitor pathways, turning compact object transients into powerful astrophysical and cosmological probes.