  On 11 February 2016, the LIGO and Virgo scientific collaborations announced
the first direct detection of gravitational waves, a signal caught by the LIGO
interferometers on 14 September 2015, and produced by the coalescence of two
stellar-mass black holes. The discovery represented the beginning of an
entirely new way to investigate the Universe. The latest gravitational-wave
catalog by LIGO, Virgo and KAGRA brings the total number of gravitational-wave
events to 90, and the count is expected to significantly increase in the next
years, when additional ground-based and space-born interferometers will be
operational. From the theoretical point of view, we have only fuzzy ideas about
where the detected events came from, and the answers to most of the five Ws and
How for the astrophysics of compact binary coalescences are still unknown. In
this work, we review our current knowledge and uncertainties on the
astrophysical processes behind merging compact-object binaries. Furthermore, we
discuss the astrophysical lessons learned through the latest gravitational-wave
detections, paying specific attention to the theoretical challenges coming from
exceptional events (e.g., GW190521 and GW190814).
