I will review the status of the space-based Laser Interferometer Space
Antenna (LISA) and its science goals. LISA will detect gravitational
waves in the frequency range 10^−4Hz<f<1Hz, a region of the spectrum
populated by a large variety of astrophysical sources. Among these, a
major role will be played by the mergers of massive black holes, which
LISA will detect up to very large redshift z∼10−20. I will focus on
the physics of these sources, as well as on how their detection by
LISA will shape our understanding of astrophysics, cosmology and
fundamental physics.