  It is thought that the final product of the gravitational collapse is a Kerr
black hole and astronomers have discovered several good astrophysical
candidates. While there is some indirect evidence suggesting that the latter
have an event horizon, and therefore that they are black holes, a proof that
the space-time around these objects is described by the Kerr geometry is still
lacking. Recently, there has been an increasing interest in the possibility of
testing the Kerr black hole hypothesis with present and future experiments. In
this paper, I briefly review the state of the art of the field, focussing on
some recent results and work in progress.
