  Geometrical inequalities show how certain parameters of a physical system set
restrictions on other parameters. For instance, a black hole of given mass can
not rotate too fast, or an ordinary object of given size can not have too much
electric charge. In this article we are interested in bounds on the angular
momentum and electromagnetic charges, in terms of total mass and size. We are
mainly concerned with inequalities for black holes and ordinary objects. The
former are the most studied systems in this context in General Relativity, and
where most results have been found. Ordinary objects, on the other hand,
present numerous challenges and many basic questions concerning geometrical
estimates for them are still unanswered.
  We present the many results in these areas. We make emphasis in identifying
the mathematical conditions that lead to such estimates, both for black holes
and ordinary objects.
