It is well known that the three parameters that characterize the Kerr black
hole (mass, angular momentum and horizon area) satisfy several important
inequalities. Remarkably, some of these inequalities remain valid also for
dynamical black holes. This kind of inequalities play an important role in the
characterization of the gravitational collapse. They are closed related with
the cosmic censorship conjecture. In this article recent results in this
subject are reviewed.Comment: Invited review article for General Relativity and Gravitation. Based
on my plenary lecture at GR20 and the longer review article Classical and
Quantum Gravity, 29(7):073001, 2012, arXiv:1111.3615. 27 pages. 14 figures.
Minor change
