  It is now well-established that a dark, compact object (DCO), very likely a
massive black hole (MBH) of around four million solar masses is lurking at the
centre of the Milky Way. While a consensus is emerging about the origin and
growth of supermassive black holes (with masses larger than a billion solar
masses), MBHs with smaller masses, such as the one in our galactic centre,
remain understudied and enigmatic. The key to understanding these holes - how
some of them grow by orders of magnitude in mass - lies in understanding the
dynamics of the stars in the galactic neighbourhood. Stars interact with the
central MBH primarily through their gradual inspiral due to the emission of
gravitational radiation. Also stars produce gases which will subsequently be
accreted by the MBH through collisions and disruptions brought about by the
strong central tidal field. Such processes can contribute significantly to the
mass of the MBH and progress in understanding them requires theoretical work in
preparation for future gravitational radiation millihertz missions and X-ray
observatories. In particular, a unique probe of these regions is the
gravitational radiation that is emitted by some compact stars very close to the
black holes and which could be surveyed by a millihertz gravitational wave
interferometer scrutinizing the range of masses fundamental to understanding
the origin and growth of supermassive black holes. By extracting the
information carried by the gravitational radiation, we can determine the mass
and spin of the central MBH with unprecedented precision and we can determine
how the holes "eat" stars that happen to be near them.
