What gravitational-wave observations and electromagnetic surveys reveal about the population of compact binaries

In the years since the first experimental detection of gravitational waves, the number of observed compact binary mergers has grown dramatically, with well over 100 detected black hole and neutron star mergers following the latest LIGO-Virgo-KAGRA observing run. Gravitational-wave observation is thus maturing into a fully-fledged tool for surveying the compact binary population, one that complements what can be learned from astrometric, radio, and x-ray observations of compact objects. In this talk, I will review what gravitational waves have taught us so far regarding the population properties of compact binaries: their masses, spins, and spatial distribution throughout the Universe. I will describe how these conclusions relate to results from electromagnetic surveys of compact objects, and along the way highlight open questions that remain unanswered or under debate.