  Soon after the observation of the first black hole binary (BHB) by advanced
LIGO (aLIGO), GW150914, it was realised that such a massive system would have
been observable in the milli-Hz (mHz) band few years prior to coalescence.
Operating in the frequency range 0.1-100 mHz, the Laser Interferometer Space
Antenna (LISA) can potentially detect up to thousands inspiralling BHBs, based
on the coalescence rates inferred from the aLIGO first observing run (O1). The
vast majority of them (those emitting at $f<10$ mHz) will experience only a
minor frequency drift during LISA lifetime, resulting in signals similar to
those emitted by galactic white dwarf binaries. At $f>10$ mHz however, several
of them will sweep through the LISA band, eventually producing loud
coalescences in the audio-band probed by aLIGO. This contribution reviews the
scientific potential of these new class of LISA sources which, in the past few
months, has been investigated in several contexts, including multi-messenger
and multi-band gravitational wave astronomy, BHB astrophysics, tests of
alternative theories of gravity and cosmography.
