The observation of compact binary mergers by the LIGO/Virgo/KAGRA collaboration marks the dawn of a new era in astronomy. Next-generation ground-based detector (Cosmic Explorer and the Einstein Telescope) will allow us to peer far deeper, and LISA will expand our gravitational wave "senses" by opening a new window at low frequencies. Observations of the gravitational waves emitted by compact binary systems in these two frequency windows can lead to new astrophysical insights and new tests of strong-field gravity. I will highlight some of the new challenges and opportunities presented by next-generation detectors. If time allows it, I will discuss: (i) the challenges of parameter estimation in the presence of waveform systematics and multiple overlapping sources, (ii) improvements in tests of general relativity, and (iii) the current observational status of black hole spectroscopy.