  I review the scientific potential of the Laser Interferometer Space Antenna
(LISA), a space-borne gravitational wave (GW) observatory to be launched in the
early 30s'. Thanks to its sensitivity in the milli-Hz frequency range, LISA
will reveal a variety of GW sources across the Universe, from our Solar
neighbourhood potentially all the way back to the Big Bang, promising to be a
game changer in our understanding of astrophysics, cosmology and fundamental
physics. This review dives in the LISA Universe, with a specific focus on black
hole science, including the formation and evolution of massive black holes in
galaxy centres, the dynamics of dense nuclei and formation of extreme mass
ratio inspirals, and the astrophysics of stellar-origin black hole binaries.
