Gravitational-wave astrophysics is now a reality. Since their first detection in 2015, gravitational waves from about 90 black hole and neutron star collisions have been observed, with hundreds more anticipated in the ongoing LIGO-Virgo-KAGRA observing run extending through 2024. Accordingly, gravitational-wave science today stands at an inflection point, transitioning rapidly from a data-limited field in its infancy to a data-saturated field, one in which the largest advances will come from the development of new statistical and computational techniques and not just by more data. In this talk, I will summarize the state of gravitational-wave science and highlight the plethora of open questions that remain concerning the origin and evolution of stellar-mass compact binaries. Along the way, I will seek to describe typical approaches to gravitational-wave data analysis today, and discuss several efforts to develop and apply new data analysis paradigms in order to accelerate discovery in the “big-data” era of tomorrow.