Roughly 100 compact binaries have been found in LIGO-Virgo data. These offered a glimpse of the distribution of black hole and neutron star masses and spins, and how they might connect to the astrophysical processes that formed these compact objects. However, these data opened as many new questions as they answered. In this talk, I will focus on the potential exciting results coming next from gravitational-astrophysics. In doing so, I will also talk about the main challenges associated with the characterization of individual gravitational-wave sources, as well as of the whole population.