  I review recent studies about the gravitational potential and stellar
dynamics of M87 in particular, and the dynamics of the stars in the presence of
a super-massive central black hole, in general.
  At large radii, investigations of both the X-ray emitting gas and the
velocity distribution of globular clusters indicate the presence of large
amounts of non-luminous matter, possibly belonging to the inner parts of the
Virgo cluster.
  At small radii, there is no evidence from the stellar kinematics, at most a
hint, for the existence of a central point mass, whereas the gas dynamics
reveal the presence of a highly concentrated mass in the centre of M87,
possibly a super-massive black hole (BH). Given the existence of such a central
mass, the stellar kinematics indicate a strong tangential anisotropy of the
stellar motion inside a few arcseconds. The implications of this result for the
evolution and formation history of M87 and its central BH are discussed. I also
discuss in more general terms the structural changes that a highly concentrated
central mass can induce in its parent galaxy.
