Testing the Kerr Black Hole Hypothesis

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 are some indirect evidences suggesting that the latter have an event horizon, and therefore that they are black holes, a proof that the spacetime 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, focusing on some recent results and works in progress.