The LIGO-Virgo-KAGRA Collaboration has observed over 70 gravitational-wave sources to date, including mergers between black holes, neutron stars, and mixed neutron star—black holes. These neutron stars and black holes connect many astrophysical puzzles, including the lives and deaths of stars, cosmic chemistry, and the growth of structure. Furthermore, gravitational waves from these mergers directly encode their distances, allowing us to measure the expansion history of the Universe. I will describe some astrophysical and cosmological lessons from the latest gravitational-wave discoveries, and discuss what we can expect to learn from future multi-messenger observations.